If a basketball player gets the ball hit from his hand on a drive to the basket loses possession but the ball doesn't hit the floor can he catch the ball in the air and score the basket?

If the loss of possession is "caused" by an opponent hitting the ball away (including hitting the hand that is on the ball and knocking it away), the player who lost possession can retrieve the batted ball in the air and play on. Not only can he catch the ball in the air and score, as you suggest, but he can simply retrieve the batted ball and regain control on the ground to set up another play. If he initially loses control of the ball without anyone else forcing the loss of control, it depends if he takes more steps to retrieve the ball or not. If he cannot retrieve the ball without taking more steps, he will be in violation of the traveling rule.