I've run across people with these kinds of questions as well. The answer to "Why does God allow good people to die?" is that God allows everyone, good or bad to die. Death is a direct result of the fall of Adam and Eve. Everyone has a day that they are ordained to die, and there is nothing we can do about it. The bigger question is "Are you ready to face God when you die?". As far as why doesn't God heal amputees, there is a whole website about this and it stems from atheism. I think the point behind that question is that even though many people will say that God healed them for this reason or that, a skeptic will doubt this and say that if God is really behind any healing, why not heal what is impossible to cure through modern medicine.
I know some will disagree with this, but we don't live in a time of healing and miracles, not that God can't heal or do miracles. Certainly, God can heal when someone prays and asks for healing. But in the day of the apostles, miracles were a sign. Today we have the bible and don't need signs. People will always throw out question designed to stump christians, such as "If God can't sin doesn't that mean He isn't Omnipotent?" It's okay not to have the answer to a question. I think Satan wants to distract us to discussions that are meaningless so that we don't talk about the basics of the gospel, which is the most important thing a non-believer wants to hear. Don't get me wrong....I get pulled into these kinds of discussions too and it's reasonable to answer a genuine question.
