If you were watching a child being raped, would you interfer ? Wouldn't you regard doing so as a moral action ? Wouldn't you regard not doing so as an immoral action ?
Then why are many rapes prevented by circumstances that are presumably under God's control?
Before I get to pointing out the disanalogy between God and us I want to explain the concept of intristic goods. As I said already, freedom of the will is an intristic good such that it is better to have a world of free agents that do good and evil than to have a world of automata that are programmed to only do good.
Further more, an even greater intristic good is to have a world in which these free agents are free to mold their characters and the world around them (which results in there being evil in the world) than to have a world in which these free agents are only free in attempting to do evil (wherein all attempts would fail and so they would be completely restricted in their molding the world around them as well as, to a lesser degree, their characters).
Finally, the greatest intristic good of them all is to have a world in which free agents who are capable of molding their characters and the world around them for good or evil choose to mold it for good rather than evil and come to, despite being faced with horrible evils that result either from moral or natural sources, know God and enter a loving relationship with Him along with their fellow humans.
Given such a framework, I think I can provide adequate answers to both of yours questions. As far as the question of "Why does God not prevent a certain evil when we ought to" goes, the answer is that unlike God we cannot assess the full value of these intristic goods while an omniscient being supposedly could and are blinded in part by our specism. (Hardly anyone bats an eye when a lion rapes another lion.) Also, God, being a provident deity, has so ordained the world to have just the right amount of good and evil so as to create the world of most intristic value. Given such a state of affairs, it would be actually morally wrong for God to change this balance which results in an overall better world in favor of accomplishing a lesser good. In a way, forsaking a greater good in favor of a lesser good which down the line produces worse results would be the truly evil thing to do.
Unlike God however, man is mandated (by God, no less) to prevent all evil he is capable of preventing thus excercising free will to help bring about a state of most intristic value. Also, our duty to prevent a given evil is because we do not know which evil will result in a world with more intristic good and, either way, as far as we're concerned, these results could only come from us failing to stop it after trying, for it is better to have a world in which an evil wasn't stopped even though we did all we could to stop it than a world in which an evil wasn't stopped because we didn't even try to stop it. It is our doing the most we can to be the best moral agents that increases the intristic value of a given world.
Similarly, the question of "Why do certain evils occur and others are prevented by circumstances outside of man's control" can be answered by pointing out that the evils that occur are sufficient for creating a world with the right amount of intristic good and in which adding further evil would result in a state of affairs which is more destructive than constructive, ie being less intristically good.