The Throne of David doesn't activate until all other abilities have completed after an evil character blocks. In the first scenario, King of Tyrus negates the banding, so it's as if King Amazing was never in battle to begin with, so TToD would not activate. In the second, again, TToD doesn't activate until the evil character's ability completes (which, in this case, includes the side-battle), so if Amazing is returned to hand during the side-battle, he's not in battle when TToD checks to see if it can activate.