Medical (child) support

What is the name of your state? Illinois

The state of MO is trying to claim some $3600 in past medical support for my daughtor. Some of these charges include her birth. My questions are:
1) Can the state sue me for child expenses incurred while I was with the mother?
2) Our son has been living with me for the last 4 years and our daughter with mother... isn't there some sort of 50/50 rule for medical expenses? As far as child support goes, we are even... but what about medical?
3) My daugher in 10 yrs old... I heard that there is a 2 year limit for the state to collect expenses from the birth of the child... is this true?
4) This is kinda vague... but a lawyer I paid for consultation also said that the state of MO has no presidence on the matter... said that they couldn't take anything from me as he tapped his finger on an extreemly thick book with either and orange or red cover. Looked like a state law book or something. Any idea what he was refering to when he said this...

Court is on 10-31-03 at 9:am...