If a receiver catches the ball in the end zone does the ball have to cross the goal line to be a touchdown?
No, and this is, as good an explanation as I can give to that question. If a receiver catches the ball in the front corner of the endzone closest to the field, with both of his feet in bounds but the ball is out of bounds and never went through the endzone as far as the pylon is concerned, it is still a touchdown due to his feet being inside the endzone.
Yes. This came up in one of the Steelers' games last year. The receiver's feet were inside the end zone when he caught the ball, but his arms were extended out into the field of play to make the catch. There was some controversy about whether he ever pulled the ball across the plane of the goal line. If he hadn't, the touchdown wouldn't have counted.
It doesn't matter where the player's body is. It only matters where the ball is. The ball has to break the plane of the goal line, regardless of where the player is standing on the field.