Also, 7-1-6
Handing the Ball Forward
ARTICLE 6. No player may hand the ball forward except during a
scrimmage down as follows:
a. A Team A player who is behind his scrimmage line may hand the ball
forward to a backfield teammate who is also behind that line.
b. A Team A player who is behind his scrimmage line may hand the ball
forward to a teammate who was on his scrimmage line when the ball was
snapped, provided that teammate left his line position by a movement
of both feet that faced him toward his own end line and was at least two
yards behind his scrimmage line when he received the ball (A.R. 7-1-
6-I)
So, to answer your questions: Fumble, Yes, Yes.