My question involves paternity law for the State of: Tennessee

I am in a relationship with a woman that is going through a divorce. She is pregnant and we both know the baby is mine. I have recently found out some interesting information about how long her husband will be considered the "legal" father after a divorce is final.
I already intended on filing a paternity suit to prove that I am the biological father.
Only problem is, I don't even know where to start.

1) Do these proceedings go throught the Juvenile Court system?
2) Can these proceedings be started prior to the birth of my child?
---I do not want any type of testing done on my unborn child!!!
3) How long after my child is born do I have to get the proceedings started?
4) Can the other guy contest these proceedings? If so, how do I fight that?