"Why would an all powerful and compassionate God allow these things to happen? Is this a nonsensical test of belief?"
I have been a Christian (or at least try) for the last 5 years. What I know is that God created every one with a free will. It was these men's free will that caused this madness. I have found that God does not allow evil of this kind to last. I also know about my God that these murderers will be punished for knowing the right choices and choosing such an evil path.
For every evil Satan or his followers commit, God rights it 100 fold. I have seen this in my personal life and speak by experience. Hope this helps.
That's my point, apparently then this was a test of belief..Why for what purpose?