[Rich1]

Assuming that the OP intended the question to be about a player who is "shooting at the wrong basket" and therefore ignoring how said basket is labeled, then I posit the following for consideration:

The legality of #1 would depend on what he did before he let go of the ball and what he did after he caught it. This could be a traveling violation if he moved without starting a dribble (but not just because he threw the ball in the air and then caught it). Since this is not a TRY then any dribble/pivot situations have not ended. Most likely would have to be a judgement call. See 4.44.3D(b).

In #2, a player who has been fouled will only shoot free throws at their own (correct) basket; never at an opponents basket unless you have screwed up. And, we would only be shooting free throws in this situation if his team was in the bonus.

Also in #2, the basket would not count because, since it is not a TRY, the ball is dead when the foul occurs. It does not matter if the ball has been released or not -it is no different than a ball in the air that has been passed between teammates. Another way to look at it is to consider that if the shooter would not get two free throws if he was fouled and missed in this situation then the basket won't count if it went in. See 4.41.2