Simulated Fumble Foul

[Reffing Rev.]

4th and 5 at B's 25. A1 running near the sideline at B21 realizing he's going down before the line to gain simulates a fumble by pitching the ball forward, the LJ correctly flags an illegal forward pass. The "fumbled" ball bounces around and then B1 picks the ball up off the ground at the B30 and runs for an apparent touchdown.

Question 1: Can B keep the touchdown?
Question 2: Can B keep the touchdown and enforce the penalty on the try or subsequent kickoff.
Question 3: If B cannot keep the touchdown, where can B take the ball?
Question 4: When does the ball become dead?

Explain.