Ok heres how it goes:

I have a Terra and a Beast Boy and he has a Magneto 5 drop and a Hassim. I have a face up USS Argus. His combat starts, uses Magneto's effect on Terra. I chain his effect with her effect and stun Hassim through USS Argus, and he then changes the target to Beast Boy. Can he do that? I think not because the target was made and he lost the effect when not completed, but he says his target was illegal. But it was legal when made, now he lost the target. Who is right?

The target is still legal and you can not change it just because it will no longer help you strategicly.

In short targets are choosen upon annoucements and can not change.

Yeah, it doesn't say to exhaust a READY character, just to exhaust a character. Sure there's not effect from the exhausting since they're already that way, but it's still a legal target.