Is it reasonable to drop weekday visits & ask for weekend? Rotating long then short? Ex. Fri-Sun 6-6, next weekend Fri-Sat 6-6?

You have to show that it's in the best interests of your child.

Can I move out of state without petitioning the court or so I still have to ask for permission to move? We all live in Illinois.

Unless there is an agreement, you need the approval from the judge. Sounds like you have a good case. Call a lawyer to discuss.

How can I legally do adoption so the birth father cant come and take the baby away?

Your best course of action is to contact a local attorney who does adoptions. Best of luck.

Can I just write her a check? For any reason could that come back on me in the future?

Yes, if you're decree says that you are to pay through the state, then you must pay through the state. If you don't, then this could cause problems...

Can I do anything about this violation in court and custody hearing or will I just have to keep induring this mans verbal abuse?

Of course not. Have your lawyer go after him. If you don't have a lawyer, get one.

What should I do with that situation and Can I still file divorced because we're both agree to everything?

If everything is agreed and there is an acknowledgement that you are not the father of this child, then you can file in Illinois.

Can one spouse be entitled to alimony if equivalent income and no kids?

Based on these facts, no. There would have to be a disparity in the incomes.

What would it cost for me to get this done? And is there lawyers out there willing to do this?

You certainly should consult with a lawyer regarding this.

Yes, it is possible to use that Facebook post. If you don't have a lawyer, you should really consider retaining one.

Divorce schedule for prove up this Friday, issue regarding 25 mile radius from old residence.

If you don't, you really should have a lawyer representing you. There is a lot at stake here.