As this isn’t criminal or civil I would say no. He was elected to public office and knew the rules of the game before he signed on. As Impeachment holds no other value than being kicked out of office he has no right to a lawyer. Also it is up to his supports in the senate to defend him.
Yes, I think you're right. The language of the Illinois statutes is clear. I would say that the law here seems to violate the spirit of our Constitution, but I guess that's another argument for another time.
I'm not sure. You're probably right from a purely Constitutional view, but we do have all those nasty USSC decisions that we supposedly must consider also. And the analog that comes to mind is that of a student suspended (gasp) from school.
ML/NJ