I believe that those were removed. Not sure.
No, still there. (You're probably thinking of Justice Moore of the Alabama Circuit court and his Ten Commandments monument.)
The thing about the Decalogue on the doors is that they're part of a collage of many historical written laws, like the Code of Hammurabi. But the fact that ancient Babylonian laws grace our highest court is not a basis for the argument that the US government advocates the worship of Marduk.
Me, when I want to know the basis for our government, I look at the document purported to be just that: the US Constitution. And what do I see? "Congress shall make no law respecting an establishment of religion, or preventing the free excercise thereof."
So, go excerise your religion all you like (just as long as "excercising" it doesn't mean persecuting others.)