I am enjoying this dialog. I have to agree with you that most of the time when prayers are answered, the answer falls in the realm of normal chances, within what would be expected probablistically speaking, nothing really out of the ordinary. Thus, there's no way to know for sure intellectually speaking, if God answered the prayer or if "lady luck" was in our favor. It takes a leap of faith to believe that God answered our prayers under these circumstances. But then there are the prayers that are answered where the answer falls outside the realm of what would be expected by chance. For example, the answer to my prayer that I posted easily falls outside of what would be expected by chance, the chances seem to be somewhere between 1 in 100 and 1 in 10,000. At this point it is more difficult to defend the position that the answer was due to chance. And then there's the case of a woman I know who was healed of brain cancer after praying. Brain cancer has a high fatality rate but I'm not sure how high it is. If it's greater than or equal to 95%, then her healing would fall outside the realm of chance, = or > 20 to 1. Of course, one could argue that her healing was a textbook case of the mind's ability to heal the body, and that the healing came from her mind and not God. At any rate, most answers to prayers require a leap of faith to believe them.
You said "This one has always bothered me. How can God have a plan for humanity, but give him free will. They don't fit together. It seems the free will of humanity would disrupt the plan of God. I know that I could be missing the "bigger" picture, but small things forever change the complexity of the larger happenings. If God knows our behavior before we do it then he isn't really looking out for us - is he?"
Yes, this one has bothered a lot of people, including me. Why would God allow humans to do evil to others and to their environment if God cares about us humans? It's actually about freedom and real love. Real love involves that the two parties involved are free to love. It's sort of like the saying, "if you love someone, set them free" (from Sting's song). True love cannot exist without the freedom of choice including the option to choose evil.
Albert Einstein was bothered by the idea that if God knew everything that will happen, how can free will exist since God knows the actions of a person before they do anything, including evil deeds. I believe that God does know everything yet free will exists. I believe that God knows all possibilities of an outcome before we choose that outcome.
If evil exists, isn't God responsible in someway since God created free will? If one believes that all possible worlds exist in the creative mind of God then it's logically necessary that there will be evil in some of those worlds yet God would not be responsible for it since in God's infinite creativity all possible outcomes exist in God's mind. I do believe that God will guide the human race to victory over evil one day but it will take time and patience on the part of us humans.