In my experience, if the guy is considering only you and you have the schollie offer out, he will sign w. out waiting. The only occasions where I've seen a recruit considering only one school and continue to wait are (1) a human school that didn't have a schollie offer out or (2) a sim.
As for #2, yes, that player would eventually sign w. Team B.
al, players are always eligible right away at DIII, so there is no chance they will go juco.