Q. I’m wondering if my fiancé can claim me, our newborn, and my son from prior relationship as dependants and claim head of household?

A. The newborn qualifies his parent (your fiancé) for dependency, head of household, child tax credit and Earned Income Credit. This assumes they lived together for more than half the year (or half the time since birth).  You and your son only qualify for the "Other dependent credit" and then only if you lived with your fiancé all year. See full rules above and here 

https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...

Q. Or would he not get the child tax credit (CTC) for my son I had before meeting him? 

A. Correct, because he is not related to that child. The child MAY qualify for the $500 "other dependent credit", but not the child tax credit (or the earned income credit). After your marriage, he will qualify for the CTC.  A step child is the same a s a biological child, for taxes.