Good work to everyone who has already posted responses to these.

With a bit of thought, the answers to all of these questions are rational, and there is plenty of positive evidence (especially for Jesus' resurrection, and for Design in Physics, for example) – it's a popular (and false) stereotype that the Christian worldview is 'irrational'. Universal Reconciliation is a great tool, also, for some of these questions!
No-one needs to be concerned when questions like these come up! Atheism is imaginary, not God!
(Sorry, the following post is quite long…)Q1Why won't God heal amputees?
Answer to Q1: I disagree with this; if we think about it, every single disabled amputee will ultimately be healed in the eventual reconciliation and bodily resurrection in the New Creation. Therefore, it is just a matter of time before every single prayer (in good intention) made by everyone will be answered in full (in the best way), with any wait only allowed for the eventual benefit of the individual (as an act of love by the Father, in a similar way to how a parent on Earth may postpone giving a child something if they knew that it would ultimately benefit them). Every person is treated with love by God, without exception. This makes the question a generally false one.
Regardless, it is quite possible that a) Jesus did heal amputees during His time on Earth, which is supported by the evidence for the resurrection, b) God implicitly heals people by preventing them from being maimed in the first place (it is possible that this 'implicit healing' has taken place many millions of times), even if they don't realise His intervention and c) there are some very interesting cases:
One was where, after prayer, 4 inches of bone regrew in a very badly injured leg (there is video testimony from the family) that was thus not amputated, as it otherwise may have been (see
http://www.rogerwebb.org/testimonies/removedbonegrowsback.html)
Another is a possible actual documented case of the restoration of an amputated leg, with some interesting evidence to go with it in Calanda, Spain (even reported on Wikipedia):
http://en.wikipedia.org/wiki/Miracle_of_Calanda.
However, far above the healing of amputees, we have very good evidence for something much greater: Jesus' bodily resurrection (see later for a case on this)
Sub topics
We believe in answered prayer, so why is a prayer for a raise etc. not have the same effect as a prayer of a starving person.
Q2Why are there so many starving people in this world?
Answer to sub-topic and Q2: Firstly, it is having an effect: prayer works on the person doing the praying (acting as a channel by which God can, perhaps, inspire them to give more money to charity), and, as per earlier, all starvation and famine (especially for the poor people who suffered it) will be ended and hence all such prayers answered in a spectacular fashion. Again, there may be a pause for some ultimately loving reason (where, in light of eternity, such a reason could be very substantial indeed), but it shall ultimately be answered. In addition, we again have the case that, it seems to me, God is constantly sustaining the universe, intervening even when we don't end up perceiving it, and so far more famines have been prevented than allowed to take place.
Q3Why does God demand the deaths of so many innocent people in the Bible?
Answer to Q3: Now, in this following way I may be making use of a principle that is contentious, but I presently advocate a method of thinking about the inspired text in the Bible that I could call 'agape-centred hermeneutics', where, after taking into account other factors, an 'agape test' is given, where the literal meaning of the verse is considered to see whether it fits into the well-documented principle that "God is love". If it doesn't fit with this, it is quite plausible that it may not be referring to a literal event, but figurative language (like a parable, which is just as meaningful and inspired); this is how I presently view some of the more difficult passages in the Old Testament, where it seems to me that such events as the harsher laws and events may not be referring to literal (i.e. historical) implementation, but instead more in the form of a parable. This wouldn't remove from inspiration, but allows passage over many problems. Then, in the context of eternal life, the mystery of such verses would gradually be unfolded to ultimately see the clear picture of God's love behind them.
In this way, I think that the charge against God in Q3 is false. I know that this interpretation method may be contentious, but at least it prevents people being turned away from Christianity on the basis of such passages (which may distract from the much greater importance of Jesus).
Q4Why does the bible contain so much anti-scientific nonsense?
Answer to Q4: I disagree again. Personally, I take Genesis to have (very important) figurative meaning, such as, primarily, God's Creation of the universe and life, but also, it seems to me, the equality of man and woman (as shown by the fact that the man is the one who did worse, sinning of his own accord, while Eve did it more as a result of deceit) and the stewardship of life. The mechanism for this creation can be disagreed about, but there is no need for controversy. I personally concede to guided evolution, i.e. creation through Darwinian evolution, where the 'random' processes were actually guided by God to bring about purpose.
I disagree with a literal flood, instead interpreting the passage to be a very important parable (still inspired by God) alluding to baptism and repentance, for example. However, anyone who wishes to disagree with this interpretation is free to do so: there is the potential for a local flood, for example.
Q5Why is God such a huge proponent of slavery in the bible?
Answer to Q5: Yet again I disagree. It seems to me that modern conceptions of slavery, where slaves were kidnapped from their former countries, is actively prohibited by the Bible (since kidnapping is prohibited, as is stealing, which should include, of course, human life). Israel were actually released from slavery! Clearly, God abhors slavery; the references to allowing it, in my opinion, would refer only to voluntary servitude rather than forced slavery, and the idea of man being made in "the image of God" ought to instantly demolish any forms of discrimination that can lead to forced slavery, or treating people as 'property.
Hence, I disagree with Q5: God abhors anything which is hateful and harmful, which is what slavery is.
Q6Why do bad things happen to good people?
Answer to Q6: With Universal Reconciliation, this question becomes much easier to answer. It seems to me that evil is a product of the misuse of free will on creatures with 'transworld depravity' (Alvin Plantinga's term referring to the idea that, no matter what situation God placed certain free creatures in, they would do at least one wrong). It also seems to me that it is possible that non-human beings (of whatever sort) could be entirely responsible for natural evil, hence reducing all forms of evil to moral evil. Then, it is only allowed to the extent that, in the context of eternal happiness, every wrong ultimately brings about, for every single individual (so no person is used as a means to an end), a wonderfully greater good. In this way, the allowing of temporary in a loving manner is not in contrast to God's goodness.
In addition, this question is interesting on its own, since it presumes a standard of 'good' and 'evil' by which to measure the world. Yet this cannot be done without an objective set of morals, set as ideas within a necessary Mind, which is God; the atheist worldview has no real justification for objective morality (although, of course, atheists still behave as though there were an objective morality). Hence, the Problem of Evil cannot be put forward unless we first presume the existence of God in the first place, and hence it utterly fails to contradict the idea of God's existence, only offering up a real challenge to God's goodness, which is not a very powerful challenge for the reasons stated in the above paragraph.
This can actually become the moral argument: if we want objective moral values (e.g. 'racism is wrong') that are justified and grounded in reasoning, we require God as a necessary (impossible to fail to exist) Mind whose will determines the morality of actions
Q7Why didn't any of Jesus' miracles in the bible leave behind any evidence?
Answer to Q7: There is certainly evidence for the main miraculous event of the New Testament: the resurrection of Jesus the Christ, which I have adapted from a post that I did elsewhere:
I think that the evidence for the resurrection is often underestimated. A case for the resurrection can be made using mainly a few facts that the significant majority of scholars (atheist to Christian) agree upon (the minimal facts method), even if we take the Gospels and Paul's letters as just historical sources rather than presuming inspired content:
1) Jesus was crucified on a Roman cross (as evidenced by Tacitus, Josephus and Paul, amongst others)
2) The disciples, subsequent to the resurrection, had experiences which they sincerely believed to be those of the risen Jesus (as seen in the very early creed contained in a passage in 1 Corinthians 15)
3) James, Jesus' brother, who is recorded as being a sceptic in the Gospels (where the criterion of embarrassment supports the authenticity of this) became a Christian, and the persecutor Paul, after experiencing what he sincerely believed to be the risen Jesus, became a devoted preacher of Christianity.
The above have general scholarly consensus (as compiled by research of large numbers of qualified scholars by Dr. Gary Habermas), and so can be used as the 'building blocks' of any explanation to explain them.
Well attested also is the idea of the empty tomb, due to the 'Jerusalem factor': because early Christian preaching was in Jerusalem, and Jesus was buried near Jerusalem. If the Jewish officials had wanted to destroy the upcoming Christian Church, all they would have had to have done would be to show them Jesus' body (had it not been resurrected); doing this could have destroyed the movement. Yet they didn't do this, and Christianity grew! The sensible conclusion from this is that the tomb was indeed empty, baffling the officials.
Then, we can use the following historical criteria, which are important to help moderate explanations that are posited:
**Explanatory power** – can the explanation explain the evidence easily, without forcing it to fit?
**Explanatory scope** – can the explanation explain all the known data?
**Ad hoc assumptions** – are there any assumptions with no evidence whatsoever that must be made?
**Plausibility** – is the explanation plausible in itself?
One old objection is that Jesus didn't actually die, and so 'woke up' after being crucified and somehow managed to walk back from the place of burial to the disciples and convince them that He had been raised to life. This 'swoon hypothesis' can be widely rejected (and it is rejected today even by the majority of atheist scholars). It utterly fails the plausibility criterion, for starters, because, apart from the friends recorded by the historian Josephus (who were removed from crucifixion early, and a few of them died as a result of this regardless despite good medical care), just about no-one survived crucifixion, let alone burial, let alone examination by Roman soldiers for signs of life. Even if Jesus had, however, He in no way would have been able to escape from the tomb, fight any guards present, walk to find the disciples (without being spotted by anyone as covered in blood), and then convince them of resurrection, without any professional medical attention. This is especially evident with James, being a sceptic who became a Christian. Hence, this idea lacks plausibility, and explanatory power (without forcing the facts to fit). It also lacks scope, not fitting the many resurrection appearances, not accounting for Jesus after this point (where would He have gone after He found the disciples?), and certainly not fitting Paul's conversion. Jesus' survival is also an ad hoc assumption.
Another objection is hallucination. This is also a poor alternative, as it would require the vast majority of the witness disciples to be the hallucinogenic type of person, which is ad hoc and implausible, given many of these disciples were chosen by Jesus, from a variety of backgrounds. They would also have to have been convinced that the experiences were bodily rather than the traditional Jewish idea of disembodied spirits after death in order to declare 'resurrection' out of the blue. Hence, this 'alternative' is inherently implausible, given the ancient creed's account (from 1 Corinthians 15) of many people having experiences simultaneously (500 people are mentioned at one stage, and a group this size is massively unlikely to have any multiple accounts of definite bodily experiences). The hallucination idea does not account well for James' conversion (from a sceptic), who would have doubted such experiences had they happened to others, and is also unconvincing in terms of Paul's dramatic conversion.
It also fails to account for the success of the early Christian movement (even though its followers were few), compared to other, similar movements, without making more ad hoc assumptions. The mutation in Jewish teaching about the resurrection (i.e. different ideas about how it happened to people) from the diversity of approaches prior to Jesus' death to a singular, bodily approach is also not accounted for by this hypothesis. Also, with the evidence for the empty tomb this approach becomes even less useful. Hence, it seems that hallucination hypotheses have poor explanatory power (forcing the facts to fit) as well as very little explanatory scope, especially with the evidence for the empty tomb.
In stark contrast to the above, agreeing to the resurrection has explanatory scope and explanatory power that instantly explains all the facts (together with many others) with absolutely no forcing. Due to the other theistic arguments that there are, the plausibility (by God's intervention, not by natural means, as the latter would not be plausible) is sufficient and it contains no non-evidenced assumptions.
Therefore, the best historical explanation for the consensus of facts is the bodily resurrection of Jesus Christ. Q8How do you explain the fact that Jesus has never appeared to you?
Answer to Q8: I disagree again: Jesus has become present in the life of any person who genuinely calls upon God, as is often evidenced by their radically changed habits and attitude, through the Holy Spirit and through the Bible. Indeed, all Christians, whether UR, ET, ED etc., are members of the Body of Christ, with all other people analogous to lost sheep, future members. Some people have had visual perceptions of Jesus, but this is not necessary for a person to experience Him. Regardless, even if we have absolutely no experience of Jesus, this will ultimately be turned around in the New Creation, with the postponement only for loving purposes of God. Hence, this question really is not too significant.
Q9Why would Jesus want you to eat His body and drink His blood?
Answer to Q9: Jesus is, of course, not just a human: although He had a human nature, He was fully God. Thus, in Holy Communion, even if we take the reference to the Body and Blood of Jesus Christ literally, it is more God feeding us with Himself in the ultimate act of true self-giving love in Jesus. Since God is love, this feeding is on love and is a powerful symbol of the transformation of a person through trust in Jesus and calling on God.
Q10Why do Christians get divorced at the same rate as non-Christians.
Answer to Q10: Since people have been given responsibility (for the purpose of improvement and development upto the standard for the New Creation), there is no reason why a Christian couple is physically forced to remain together, as this would abrogate free will. Indeed, I have strong feelings against divorce because of its effect on the former partners and (especially) the children, as well as Jesus' injunction (but, of course, people who have divorced are just as valuable as everyone else); I think that the Christian divorce rate is more a mistake made by modern Christians than any other reflection. Potentially the emphasis on self-giving love has not been emphasised enough.
Sorry that this post was quite long! I have some material at
http://rationalchristianworldview.blogspot.com/ if anyone's interested.