This might prove to be a time bomb, considering that approximately 95% of theists won't agree with me. Prayers cannot make God change His mind, that's the point. I mean, requesting prayers. That's not simply my opinion but my understanding of Numbers 23:19 in the Torah, where we have that God is not like a man to change His mind.
Prayer, by definition, if we seriously think it through, is an attempt to make God change His mind.
Forgive me.,. I did not not read the rest of your post. Prayer is an affirmation of a state of mind, those states have a tremendous impact upon people in them. If you take out all the gods and all that, proper prayer is a meditation and an incredibly benificial state of existence. Even atheists could Benifit from the concept and the world would grow leap folds once we all adopt it properly. ( if only )