Offensive Foul after Shooting Foul?

[potato]

If A goes for a shot and B blocks & commits a foul, while still airborne, A pushes B away and makes the shot, would A be called for a foul or game stops when the defense commits a foul and a free throw awarded, or would A be awarded a free throw and A takes a foul and ball starts as if A commited a foul, but what if A missed the freethrow?

Usually double foul happens when a defensive foul is followed by another defensive foul, and rarely followed by an offensive foul, but it can happen if B fouled hard and A shoves B away to make a shot.