How can we defend our faith against the "Argument from Evil" or "Problem of Evil"? Of all of the arguments against the Bible from a stance of pure logic which I have ever heard, the only one which seems to be able to stand up to honest, logical scrutiny in even the smallest way is the Problem of Evil.

Clearly, from a Biblical standpoint, we can say that our free will, given to us by God, causes the sufferings that man brings on other men. The common rebuttal to this: that God's omniscience would cause Him to know the things we will do and thus render free will an illusion, can be shown to be invalid through some simply logical reasoning. Namely, that it is sound logic to say that "correlation does not prove (nor imply) causation", and that God's knowledge of our actions (even if it is beforehand) correlating with our choice to undertake said actions, by no means proves the causation of our actions on the part of God. We are still left with bearing the responsibility for said actions and their consequences, as God's foreknowledge of our choice does not compel us to choose that option. Furthermore, the idea that God exists "outside of time" lends support to this argument (although it is unnecessary in this argument).

Unfortunately, this argument cannot be used to explain the suffering found in nature (animals hurting animals), nor can it explain natural disasters. Is there a theologian or apologetic scholar who has written to explain a way to rationalize this? Is there anyone here who has studied this in depth and can offer a rationalization?
I haven't personally read Alvin Plantinga, but I've read that he tried to answer question of "natural evil" in a very interesting way. See some short description here http://www.iep.utm.edu/evil-log/#H6 and more in his books: "The Nature of Necessary", "God, Freedom, and Evil".

What I personally think is that there is a great problem of perception. I think that St Augustine might also went that way in his "Confessions". I think that what we perceive as "evil" is often some disordered good (or not well understood good), for everything that God created was good - even microorganisms living, fighting, suffering and dying in our bodies. 

So from where this disorder comes? I think that Moses gives us a hint. In first book of Bible he is describing some ancient events. He couldn't see it himself and we don't know how he came to have knowledge about them - maybe God or his angels directly described it to him or maybe it was brought to him in a visionary dream or maybe Moses in prophetic spirit recognized grains of truth in myths preserved by people. It is not important. 

What is important is that among other things he tells us a story of punishment, and this punishment is essentially a suffering from natural causes: pains from body, unfriendly environment. This punishment is an element of justice, it is not evil. 

It is important to make some distinctions here. For example someone could say that to kill someone is an evil thing, but this is not true. To MURDER someone is evil and when you look at Ten Commandments in Hebrew then you will see that there is no "thou shalt not kill" but "thou shalt not murder". Are there situations where killing is acceptable? Yes, there are and you can find some of them described in the Bible. You can also use your common sense: if you are suddenly attacked and you act in self defense and kill whoever attacked you then it is not considered evil. 

Similarily, it is not evil in itself to make someone suffer. But it is evil to make someone suffer without proper cause. For example, Bible recommends using force in education if it is necessary for saving someones' soul. What is REALLY evil is disobedience to God. And that was not created by him, for he is not disobedient to himself, but this is a product of our ancestors' use of free will. 

All other things may be seen by us as "evil" but in reality they may be just misunderstood acts of justice, of punishment and of workings of nature. Natural disasters aren't evil and suffering of animals isn't evil in itself.