Most of them do. They're usually constructed as restrictions on the government's authority rather than grants of rights to a specific group of people, and there are court rulings clearly stating rights like freedom of speech and freedom from unreasonable search apply to any person subject to the government's authority.

Non-citizens don't get the right to bear arms as far as I know.

This *1000. It's a supreme failure on our educational system and society at large that most Americans don't think about our government and our rights in these terms.

The Constitution actually takes away our rights. It has to, it lays out the powers the government has over us. Even the bill of rights doesn't technically give us rights---it explicitly details the ways our government cannot operate.

I've made this point on this forum before.

These are natural rights. The constitution, as you say, delineates state powers as a necessary infringement upon those rights.

It depends on the right, some are describing "person", some are "the people". E.g. the 2nd amendment talks about the right of "the people" to keep and bear arms not being infringed and there are federal laws on the books directly barring aliens from keeping firearms so "the people" evidently does not apply to anyone everywhere in the Constitution.

Most of them do. The Constitution is clear on when it talks about citizens versus all people. The exceptions are things like the right to vote or hold federal office.

Generally yes but government can currently cancel your visa due to exercising those rights in many cases.

The constitution applies to all people under US jurisdiction. It only specifies a few citizen-only rights, like voting.