Player goes out of bound & touches the ball

[potato]

I would like to know is it considered out of bound or illegal for the following scenarios:

1.B1 goes out of bound legally (diving for ball), A1 gets the ball & attempts a shot, B1 jumps from out of bound towards A1 to contest the shot & touches the ball, would it be considered out of bound A teams ball if:
1a.B1 touches the ball A1 is in possession of.
1b.B1 touches the ball after A1 released the ball (block shot) & shot misses.
1c.B1 touches the ball after A1 release & ball goes in the basket.


2.Is there a difference between NBA & NFHS rule regarding players going out of bound saving a ball & reenters the court with both feet in bound allowed to be the 1st player to touch the ball?
If the player is allowed to do so:
2a.Does it matter if the player jumps out of bound grab the ball & throws it back inbound before player lands out of bound comes back & be the 1st one to touch the ball (would the save be counted as a pass which he cannot be the 1st to touch?).
2b.Was dribbling near the line lost his balance, pushes the ball inbound before player goes out of bound (not ending his dribble), gets both feet back in bound & continues to dribble.