First of all, you are doing the right thing meeting with a lawyer. He does have to pay child support, whether he believes in it or not, that is his child and he needs to help support him. He is responsible for half of all the debts, and the assets should be divided about 50/50 as well. visitation can work a number of ways depending on what everyone wants. Many do every other weekend and alternating holidays, along with 6 - 8 weeks during the summer. I know that this is hard on your son, but it is important that you encourage a relationship with his bio dad if bio dad is willing. If you deny him that, he will resent you later when he grows up and does not know his father.
Get him off your insurance now, and see if you can get some of the back child support and insurance premiums as part of the divorce settlement. When my parents divorced, in addition to child support my father was responsible for 50% of all medical bills, my mom had better insurance so we stayed on her policy, but if you do not have coverage he could need to supply that for the child as well. Your lawyer will walk you through all of this. You need to get a fare settlement, do not let your Ex make the decisions here, it sounds like he is trying to screw you (doesn't believe in child support!?! It is part of being a father!). You are being way to nice (keeping him on your insurance ect..)it is time to focus on you and your child and make sure you get what you need from bio dad to take care of that child's needs!