NF: A1 has the ball on their 20. A1 throws a pass that is intercepted by B1 on 50. B1 runs to the 45 and throws ball(flag is thrown and spot of foul is bean bagged) forward towards B2, but A2 steps in and catches thrown ball and runs for a TD. What is the ruling? I can't find anything in the case book. What if this happened on Kickoff? Where ball is pitched forward and K intercepts?

The illegal forward pass by B1 following a change of possession is a live ball foul. Since it was intercepted in flight, the ball remains live and the play continues, just as it would following any other live ball foul. The ball becomes dead when A2 enters B's end zone with the ball in his possession. A would decline B's foul and take the TD.

On a kickoff, the ruling would be the same. Because the kick ended when possessed by B1, K2 would be permitted to advance the interception of B1's illegal forward pass. TD for K.

By the way, why is there a flag and a bean bag? A flag marking the spot of the foul is sufficient.

Only the flag should have been used. BJ gets bean bag happy at times saying it was for a point of reference.