Okay, my partner left when I was pregnant, so I have gone through some of this and it's hard, so I really, really feel for you.
Some of what you are asking depends on whether you are still married when the baby is born, and whether your husband's name is on the birth certificate. You need to check whether the simple fact of you still being married gives him 'rights' or not. I think it might, so find out.
I do know that actually the phrase 'parental rights' is wrong - only the child has rights. In law the parents have 'responsibilities', adn these are basically to give the child a good life. Only the parent named on the birth certificate counts in law.
When the baby is born the CSA can legally force him to pay towards the child, including stopping his wages at source and freezing his assets if necessary. However, they won't do anything before hand, so no, you can't do anything about that.
If you are not working there are various benefits, including a one-off payment for £190 and another one-off for £500 that you can get paid to you.
Speak to your local Citizens' Advice Bureau. I think you are going to need someone on side as soon as possible.
And your GP, too. Just in case it all gets too much and you need support.
Very best and many hugs to you. x