1- Yes, you can use egg from a donor, even if she is married. But she should not be your mother or sister.
2- No. It is not considered adultery, and the resulting child is your legitimate son, and is Mahram for your wife also, as she is going to breast feed him.
But is she is considered his mother or not. S. Sistani says that as precautionary action, none of the women is considered mother for the child.
But, as this is not fatwa, you and your wife can refer to another Ayatollah, who says that the woman who gives the birth is the mother.
Me and my wife have been trying to have baby for over (removed) years now. The doctor says that my wife has a very low ovarian reserve – which means chances of conceiving are very slim.
Can we use egg from a donor to fertilise with my sperm and implant the resulting embryo in my wife’s body?
Will it be considered adultery? Will the resulting child be legitimate? Will it be my wife’s mehram ?
If it is allowed can the egg donor be a married woman?