I take it you also believe, as a minarchist, that homosexuals should be allowed to "marry" each other and serve in the military and you also believe that a woman should be able to "choose" to murder her children?
If you understood the Constitution you wouldn’t be asking such stupid questions.
The States role is to protect me from harm by a neighbor. That’s it.
So because you fail to begin with the foundational thesis you instead assume the State has certain authoritarian rights to impose rules on peoples private behavior. Completely anti-constitutional.
So to answer your stupid questions from a Constitutional perspective:
a) Marriage is a religious affair. According to the Constitution people have a right to free association. That you wish to encroach on this right is telling.
b) The State has a right to prohibit homosexuals in the military if they feel that it would harm their duties to protect American citizens. Their obligation is to make sure they protect American citizens from harm in the best way possible.
c) The State has an obligation to protect babies as well as mothers. No, mothers cannot kill their babies.