Q1: I understand Wesleyan perfectionism to be rather more amiable than often assumed. The theory is not that a Christian shall attain to an utter and persistent inerrancy. It is that a moment of pure faith in God is possible and in that moment, for as long as it lasts, there is nothing in which that Christian is morally at fault: past sins are forgiven or otherwise remitted (e.g. resolved in themselves by that pure faith) and momentarily the faith precludes sin, since "whatsoever is not of faith is sin" and thus sin could only proceed from a faithlessness of which the Christian in that moment is not guilty. There are forms of perfectionism which hold a view closer to the one I think you are viewing, but I don't take Wesleyan perfectionism to be one of them.
Q2: This question is partially nullified by my answer above. Nonetheless, I question the aim and motive of such an attempt at attaining, you might say, "perfection by prayer". That we might excuse ourselves of our sins by the consolation that we can merely pray ourselves into a moral perfection and thus not really need to develop the character to will with God against those sins? I imagine the Jesus we see in the Gospels would take issue with that! Why would God give us a will, and then go to lengths to ensure that we exercise that will and grow into alignment in that will with his own will, if in the end the solution is a momentary disavowal of that will, after which we never have to make any conscious effort to continue willing God's will? It seems like the daydream of one who desires to abdicate the moral responsibility God explicitly created him to have (God is the one who created our wills -- and called them good). So, so far as I believe I have understood God in my life, his project in me is to get me to continue to grow in trust of him (to have utter faith in him), that I might be freed to will according to his will, instead of being constrained by my fears to oppose his will and affect my own salvation or immortality (whether literally or symbolically).
Q3: If I understand the concept of "pray to moral behavior" as you mean it, it seems so foreign to the view of moral development in the Jewish mind and the emphasis on obedience in the words of Jesus in the Gospels that I question whether the theory could even be taken seriously enough by the Biblical authors to be addressed directly. What I would expect to find in Scripture, then, would be an assumed understanding that such a method of moral development (if it could be called that) could not possibly fit the nature of God, nor the evident nature of humanity.
Having said that, I would make clear that I hold prayer to be one of the fundamentals of Christian life and moral development, for several reasons, not the least of which being that it is an exercise in several essential things: 1) thinking of God personally; 2) trusting God personally; 3) prioritizing one's thinking in light of matters of eternal significance; 4) thinking of and empathizing with other people than ourselves (even if only God); 5) seeing ourselves with a measure of objectivity (that is, from God's perspective); 6) seeking security and truth outside ourselves; 7) admitting we don't have all the answers and are not sufficient for ourselves (that is, humility); 8) patience; 9) reflection and self-assessment; 10) listening (depending on the case) to the Spirit, to reason, and/or to the consciences God gave us and which may be trying to win our attention.
Furthermore, I believe prayer affects God in some way. Jesus certainly seemed to believe so, as did his brother. Now, I think the common apprehension here is due to our limitation: we think of God so one-dimensionally, as if God existed according to the precise same relation to time that we do. It is not clear that our past is the same, conceptually, as God's past. It may indeed be a category error to even posit such a thing as 'God's past' or 'God's future'. Herein lies the possibility for God both to be responsive to our prayers and to be 'the same yesterday, today, and forever': God exists, as nearly as we can express in human language, ever-presently. Our past, our present, and our future are all concurrent to God. It may be that God heard your prayer in your 2004 when he was forming the foundations of the world and simultaneously was speaking as the Lamb before John and passing before Moses and watching a sunrise in the autumn in Maine in days before European settlers reached the Americas. So God's actions, taken as a whole, are responsive to his own creation, from his perspective, but from our perspective it is equally true to say that he always intended, say, to ensure that a certain person didn't die in a certain storm in 1997. So it must be said that God always intended it, but it must also be said that he always intended it because he heard our prayers from before the foundation of the world. Thus God is both changeless (he would never have done otherwise than he has done) and open (God may respond especially, to any -- or, as it may be, every -- choice of humanity, and no doubt every honest prayer).
And lest someone claim that this seems to threaten his sovereignty, I would call to their attention that if indeed God chose sovereignly to give the power of volition to his creatures, then it follows as a matter of course that he sovereignly wills that they will (else why conceive of giving us wills?). Thus the idea that we have wills, and that he may honor those wills to any extent of his pleasing (even fully), does not in itself threaten God's sovereignty. He can, if he wants, give us wills, and give our wills space to will, to some extent, and himself respond to those wills actively.