I may be an anti-theist, but I can see how prayer may be, in some cases, a form of self-reflection. For any other purpose it is pretty worthless, and certainly not all prayer could be considered self-reflection (the crazy, evangelical kind in which people pray in large groups, in churches and such.).
Self talk is sometimes useful, but I get better information when I talk to my peers and mentors. Though, self talk or prayer is useful to organize my thoughts, like how will I present my ideas for getting the best response from my mentor or get financial backing for my next project. So Yes, Self talk/prayer is self conversation.
Talking to yourself is still a conversation, I suppose. Which is all prayer is- talking to your own head. You could get the same cathartic benefits of "prayer" by writing in a journal or talking out your day with a friend.
As for "answered prayers"- I could get the same results praying to my cat.
Most people think that prayer is asking something from God. But, that's not at all what prayer is about. Praying is a much deeper experience than that. Prayer is about having a relationship with God; it's about thanking and praising Him, and letting your concerns be known to Him. .