Your rights extend only as far as the next persons. You can kill whoever you want, but we all have the right to live. By killing someone you're violating their rights and thus breaking the law. Our elected officials placed their hands on Bibles and swore to uphold the Constitution. They did not place their hands on the Constitution and swear to uphold the Bible.
CS, According to the way it's currently interpreted. Yes it would.
Most of our laws are derived from Christian Values.
See Gay Marriage, Prostitution, Drugs
Just because a law is also a sin in a religion does not make that mixing church and state. If I invented a religion tomorrow that believed everything in the Constitution (except the first amendment) to be the divine word of God, that wouldn't make the constitution void.