Player goes out of bound & touches the ball

[potato]

under the 1st scenario, would B1 be called a goaltending should he jumped from out of bounds to interrupt the ball when it's going downwards, or will it still be counted as out of bound A ball?

so in both NFHS & NBA, can i say that if the player established possession of the ball while trying to save it throws the ball back in, it shall be considered a pass thus the player may not be the 1st to touch the ball even if he's already inbound?