married but will separate when daughter is born

I believe the answer to all three of your questions is yes. Assuming she has the child in a hospital, she can request that you be kept our of the delivery room and they don't let anyone in the delivery room without the mother's ok. Since she is the one who will give the hospital the info for the birth certificate, then yes, she can keep your name off it as well. And as for the name of the child, again, they will be asking her for that info, not you, so she can name him/her (not "it" as you wrote) whatever she pleases.

The above opinion is based on my understanding and may not be absolutely correct (but I think it is). It may also depend on your state of residence.

from experience....

all it takes to add yourself to the birth certificate is a paternity test.
OR- there are forms you can fill out and submit ( depending on what state) that will include you on the birth certificate because it is legally 'assumed' that any child born during a marriage is a product of that marriage and it is up to the individuals involved to legally prove that wrong..