Thank you for your answer and waning about the terminology. Yes for the second situation, it's a catch not recovery.
Uh, in your second scenario, you don’t make it clear that the legally kicked ball, untouched by B, touches the ground in the end zone, but that is the implication. As others have said, in that case, the result of the down is an instant touchback, and any subsequent possession of the ball is moot - the ball is already dead.
In your third scenario, as others have explained, the legally kicked ball is still in flight when it comes into player possession (either team), so that is a catch. Alive if caught by B, dead if caught by A. Touchdown, if caught by A in B’s end zone. Get video.🙂
One other possibility is when the legally free kicked ball bounces in the field of play and, before touching the ground in the end zone, is recovered in the end zone. Alive if recovered by B; dead and a touchdown if recovered by A. I’ve seen both of these outcomes. But I don’t have video.😁
Robert