Does he have to pay child support?

A person only has to pay child support if there is a court order to do so. If there is no court order then no is required to pay.

The other answer had a very good point -- the only person who can order child support is a judge. Either with a divorce or if there is a finding of parentage. Illinois Statutues do not recognize "shared custody" however, if the time spent is pretty even a judge will look at the total circumstances -- incomes of respective parties; debts of respective parties; assets of respective parties; amounts each party spends on the child, etc.

Please hire an experienced Family Law attorney in your area. They will be able to tell you how the particular judges in that area will look at the situation once they know the details. The child support guidelines for one child is 20% of net income. Gross income minus taxes; social security; medicare; health insurance; mandatory pensions; mandatory union dues, etc. This can be a complicated matter and no one should represent themselves in this kind of case.