OP: Yes.
So if someone goes forward at a Billy Graham Crusade and really wants to have his sins forgiven and really wants to please God and really wants to walk with Jesus, really wants to be born again and sincerely prays for salvation, then you would have to conclude that he is, in fact, already regenerated, as no one could possibly do those things unless they were regenerated?
The best gifts are free!
Yes.
If a man's heart truly inclines towards God, it is because God in His regeneration has caused the man's heart to incline towards God.