newbie needs your comments and suggestions

Hi, I am a newbie in this forum. I realized the posts are really helpful but my situation is a little special. I hope gets some advise from you.

My "marriage" started late 2008. I have one kid apparently living with the property but I still have full finance responsibility since she did not have any income at the time. We started to discuss the divorce 3 years ago and since then we never had any sexual relationship but just lived in the same property. A few months ago, I moved out and she promised to speed up the divorce process but that did not happen.

I need your suggestion before I want taking following actions:
1. I will move back to my property since right now she is messing up my property; is there any legal issue?
2. numerous times I feel she is not normal, meaning she might have mental issue; if that's true, how could I maximize the health of the kid's growth? is it possible to ask court to do a mental health check before we get divorce? If she really has mental issues, I would like to take the kid's custody;
3. right now I am paying everything, the property, all the insurance (including their health insurance); she actually did not pay anything for the property and anything inside the property; is there anyway I can enforce her to move out but leave the kid in the property?
4. if i move back, I will bring the kid to my company's daycare; right now the kid is in another daycare and I did not issue the right; is there any legal issue?

By the way, I am living in Chicago land.

Thanks for any suggestion and comments

Michael