Congratulations on the impending addition!
No, the father is not automatically responsible for half the medical expenses. There is a way under Illinois, however, that he could possibly be responsible for ALL of the expenses related to the birth. You should hire a lawyer.
Just as an aside, if he won't communicate with you, how do you know "he states he wants a part of child's life?"
You should probably stop taking legal advice from your spouse and family. Hire a lawyer and get some real legal advice.
You don't give enough information to allow an attorney to answer your question about whether you'll have to pay maintenance.
Below are some legal articles that may help answer some of your questions, but CALL A LAWYER.
There's only one step to take: hire a lawyer.
The support will keep slipping away from you until a judge orders it to stop. That won't happen until you file the proper papers with the court. That won't happen until you hire a lawyer. So . . . you know what needs to be done.
Some "uncontested" cases costs a few hundred dollars; others cost several thousand dollars -- it depends on the size of the estate, the complexity of the agreement, and where things stand in negotiations. To most couples, "uncontested" means they don't fight anything out in court. They might fight and argue and haggle over a lot of things (like, for instance, how much child support one should pay to the other, or who gets the nicer car) but, as long as they never have to take the witness...
I don't know what a "Thai Prenup" is, so I may not be giving you a fully-informed answer.
Assuming, eventually, the prenup possibly would be enforced or contested in an American court, then it would probably be best to have it crafted under American laws. If you anticipate the agreement may eventually be needed in the Thai legal system, then it should probably be crafted with an eye toward those laws and norms.
Prenups from other lands usually are valid and enforceable in the U.S. -- so...
Assuming there aren't some other facts you're not sharing, your soon-to-be-former wife cannot pursue the "assets" (the "corpus" of the trust.) She CAN, however, go after the income from the trust for purposes of child support or for maintenance.
Get a copy of the trust document and talk with your lawyer. If you don't have a lawyer, hire one.