will they still take my birth certificate if its damaged

I don't know, make a copy of it just in case and take both

Yes, but better if you bring a passport

There's no way to answer that without seeing the document and how extensive the damage is. The DMV needs the original. A copy won't do.

Theyll need the actual copy so bring it anyways but you may have to order another one before they'll accept it.But i agree...make a copy of it and take both of them with you or call and ask before you waste a trip up there.