Can your baby have a birth defect due to a hepatitis a & b shot prior to your finding out you were pregnant?

Unrelated. Any baby can have a birth defect, but the defects have no relationship to the vaccines. Defects happen with or without the vaccines. Babies with significant defects are supposed to be automatically miscarried, which is nature's way of helping ensure that only the healthiest fetuses develop into newborn babies. Of course, there are no perfect babies, no perfect children, and no perfect adults.
Highly unlikely. Not to my knowledge from what I have heard so far.
Unrelated. These vaccines contain non-living proteins that trigger your immune system to form antibodies. They have no ability to infect you or the fetus or change how it forms.The only vaccines we avoid during pregnancy during pregnancy are the live ones, and that is out of an abundance of caution.