Any lawyers on here?- need advice

I’ve been with my boyfriend for about 3 years now he was previously married and got a legal separation from her but never divorced her. Once I have my baby will this other woman have rights to my child’s taxes? And if things don’t work out sometimes down the road who gets to claim the child on the taxes? (The mother or the father?) Also if I put him on the birth certificate does he automatically have parental rights as the father versus me not putting him on the certificate? I fear if one day things don’t work out he will try take the child from me without having to go thru court... I am a fit mom and stable just need to know some things before I make the big decision- baby is due in a month. I wouldn’t want child support from him if we broke it off or his money just need to know what I’m getting into because in the end I don’t want to get screwed over. Also if I end up putting his last name on the certificate but not putting who the father is will that be a problem?