do we give a player 3 points if he leaves the floor from behind the line, jumps forward and releases the ball before he returns to the court?

Your position on the court is the last place you were touching the court. Yes, it's a three. It's the same as saving a ball from going out of bounds. You may jump and catch the ball as you head OOB but you don't violate until you land.

that was my thinking, similar to backcourt violation. Thanks

Only if the shot goes in the basket.