Is this a b/c violation?

A1 is dribbling the ball in the backcourt near the division line. A1 dribbles off his leg, the ball bounces off B2 leg in A's frontcourt and comes to rest on the floor in A's frontcourt. A1, standing in his backcourt, reaches across the division line and secures the ball.

Based on the rule? No. A is not the last player to touch the ball prior to it gaining BC status. The instant A1 touches the ball, it gains BC status. Last to touch before that was B2.
For the record, I think the ruling would be the same if the ball were bouncing back from the FC.

How about this one? Same principal, only slightly different action:
A1 dribbling in the BC, near the division line. B1, guarding A1 and standing completely in the FC. B1 reaches and slaps at the ball, knocking it into A1's leg. Violation?

According to the rule, no. According to the interp, yes. Your call?