A1: Freedom of religion only seems to apply to Christians. If she had been a Muslim, would you have spoken up to protect her freedom of religion? If the offending problem had only been applicable to Islam, would you have tried to protect her freedom of religion?
A2: As a public servant, she refused to do her job, ignoring his rights and in conflict with the law. If she can't do her job without repressing others, she should't be allowed to hold that position. Not fight for her right to use a position as a public servant to oppress others.
A3: Allowing doctors to do the same (I'm not quite sure what you mean, but assuming that is accurate), is to say "because others are allowed to do wrong, this should also be allowed". That is classic "whataboutism", and no, neither should be allowed.
A4: It has everything to do with Democracy, since there cannot be a real democracy when only one religion is the one that is "free". That is not Democracy that is Theocracy.
B: Interesting. I hadn't read up on the classifications of "religious laws". I'll have to look into that some more.
Still, I'm not aware that Jesus said that these rules was not to be obeyed. Who then decided this?
C: "...one enters slavery voluntarily..." - No, I'm quite sure that is inaccurate.
Jesus never condemned slavery and he never even restricted the rights to slavery to the servitude variant of slavery, as you seem to be suggesting. He did suggest that masters should treat their slaves fairly, but only as long as the slaves didn't make anything to anger their master.
It sounds as if you suggesting that you are okay with slavery?