A1's pass in frontcourt tipped by B1 then tipped by A1 prior to going backcourt where A1 regains possession. Is this a backcourt violation.

Yes, as soon as A1 touched the ball in the backcourt.

yep
 

Sure is, just remember after have team control in front court it is:

"Last to Touch, First to Touch"

Re: yep
 

Actually, you have to have team control AND FC status.

Same situation without the tip by B1. Is this BC?

Yes.

If B1 tips the pass and it goes backcourt, then no backcourt violation if A1 goes back and regains possession in backcourt. Why then if A1 were to tip after B1 tips would it be a backcourt violation. A tip does not mean team control does it?

Correct.

That's why A still has team control after B1's tip.

Again, the four requirements:

1) Team COntrol
2) Ball in front court
3) A last to touch before ball goes to BC
4) A first to touch after ball goes to BC

In your first example, item 3 is not met.

In your second example, all items are met.