Presumption of Paternity: Tricare for Out of Wedlock

Ok so I'm 8 months pregnant and the father is an active member of the military. The father has made it clear that he does not wish to have anything to do with the child. He is concerned that he is not in a financial position to have another child (he already has one by another woman, which he must pay child support on). It was his wish that I have an abortion but that was something that I was not willing to do. I would like to respect his wished to not be an active parent to this child. Financially it will be a struggle but well worth it for me. I would like to ask for assistance in medical insurance (Tricare) but I do not wish to seek child support. Is it possible to do one without the other. I did not want to put the father's name on the birth certificate because I was concerned with his not being an active member of our lives that it may complicate life changes down the road for me and my child. It is my understanding that with a paternity test that I do not need to have the father listed on the birth certificate.

1. Can the child be covered by Tricare and NOT have the father pay child support?
2. Can the child be covered by Tricare without having the fathers name on the birth certificate?

Presumption of Paternity: Tricare for Out of Wedlock