More accurately, the U.S. Constitution applies to the US government, not to the people it interacts with. Some of its rules are preconditioned on dealings with certain classes of people, however, so citizenship is sometimes relevant to Constitutional considerations.

Yes that is an important clarification. Thank you.

Yes in most cases it applies to all US residents. But many don't apply to non-residents who still live in the US. For Eg: international students.

Do you have an example? I'm not saying you're wrong, I just can't think of anything off the top of my head that wouldn't apply to an international student. The second amendment comes to mind, but there are Alien Firearms Licenses available.