A1 in frontcourt passes to A2 and B1 tips the pass and it goes in the backcourt where A1 then goes and retrieves the ball. is this a backcourt violation??

no

Three elements:

1. Team A control in front court.
2. Team A last to touch in front court.
3. Team A first to touch in back court.

1. Correct, but often confused because there doesn't need to be player control in FC.

2. Incorrect -- A needn't touch the ball in FC. The correct wording is "A last to touch before ball goes to BC."

3. Incorrect -- A needn't touch the ball in the BC. The correct wording is, "A first to touch after ball goes to BC."

How about this variation?

A1 in backcourt, passes to A2 in frontcourt. The ball glances off A2's hand and goes into backcourt where it is recovered by A1.

Player from Team A was last to touch in frontcourt.
Player from Team A was first to touch in backcourt.

Over and back?

Yes.