Pay the money to one of the background sites and find out why he spent time in jail.
Go to your attorney now, even if you take no action, just to let him know the circumstance and get his advice.
Not sure about this one, but if you have a custody agreement don't you have a court appointed...
Get some help. Call around and find a minister that will do marriage counseling for free. And if he won't go, go by yourself. It's very scary to have marriage trouble and it makes it hard for you to take care of your baby.