Legal Question in Family Law in Illinois

It depend on the nature of the ruling. If is was on a substantive issue, then you are stuck with that judge, If on, for example, a motion for a continuance, then you could still change judges, The issue is very fact specific.

Yes, but only for cause. And that is an extremely high burden. Something like you saw the judge outside the courthouse and he said "I'm ruling against you because I don't like you". Simply arguing the judge is biased because he ruled a certain way will get you nowhere.