Yes, if the mother of the child puts his last name on the birth certificate.
Absolutely! You can give the baby the fathers last name even if you never married him but you must do it when you fill out the information for the babys' birth certificate when the baby is born. Otherwise, you have to go through a lot of red tape but it can still be changed.
Yes, ofcourse the child can carry the last name of the father, PROVIDED with the fathers consent as well. He have to sign a paper indication that his last name will be used by the child. It is not possible if the mother will just put the fathers surname without the fathers consent and signature in it. This is just a proof that this legally was given to her by the father. Even though they are not married. But the right of the child obviously half half of the inheritance of the fathers children from the first wife.