I think that this is a very interesting topic that brings in a debate far deeper than it would first appear. We must consider the Law of Attraction and a number of other variables before we can tackle the question of what Prayer actually is.
Now I think your questions are more posed to the effectiveness of prayer, than the actually nature of prayer. I think this quote from "Morals and Dogma" by Albert Pike explains the reason for prayer quite well.
"It is but a shallow scoff to say that prayer is absurd, because it is not possible for us, by means of it, to persuade God to change HIS plans. He produces forknown and foreintended effects, by the instrumentality of the forces of nature, all of which are HIS forces. Our own forces are a part of these. Our free agency and our will are forces. We do not absurdly cease to make efforts to attain wealth or happiness, prolong life, and continue health, because we cannot by any effort change what is predestined. If the effort also is predestined, it is not the less our effort, made of our free will. So, likewise, we pray. Will is a force. Thought is a force. Prayer is a force.
Prayer is sublime. Orisons that beg and clamor are pitiful. Yet the effects produced, when our hand, moved by our will, launches a pebble into the ocean, never cease; and every uttered word is registered for eternity upon the invisible air."
Yes I do believe Prayer has an effect. I believe that combined Prayer is even more powerful for we are all fragments of the One and when our combined wills send that force into the universe, we work as a single mind or consciousness and help to attract those desired attributes and allow it to take form in our reality. God tends to act in mysterious ways when answering these prayers . I truly believe that Prayer has a larger effect than many people give it credit for.