I do not wish to claim I can answer all of your questions with absolute certainty. However, there is nothing wrong with me giving you my opinions up to this point.
a.) Most likely. However, this could of been destroyed when Adam first sinned, which then caused man to know right from wrong. Since the first sin, God's perfect Creation was destroyed and men were no longer able to be perfect (even though they WERE created with the free will to be able to do so.)
Another scenario could be that although there still is a potential way to avoid sinning, God knows it will never happen because of his infinite knowledge. In other words, the odds may be something like 1 in 10 to the 10,000. The possibility is there, but surely you would not argue that it would eventually happen. Even if you don't consider the extremely low odds, it could also be argued that God just plain knows that a human who doesn't ever sin in his entire life will never exist.
b.) Theoretically, yes. Three possible reasons this will not happen:
1. The odds may be so low that to even consider that it would ever happen is not realistic.
2. God knows it will never happen even though it is possible.
3. Humans were originally created with the ability to not sin, but since then that ability has been destroyed (most likely by Adam's first sin).
c.) Although, God not only has the ability to see the future, but also to see the potential future. If God knows that the baby will sin under the condition that he does live, this may be enough to allow punishment. Whether or not that is fair is not for us to decide, as God is always fair and just because we don't think it seems this way does not mean that our viewpoints are true.
d.) If I had to keep one of the two, I would say free will. You can see my reasoning in the above answers.
Original sin, you ARE the weakest link. Bye-bye!