Do constitutional rights apply to non-citizens? I always thought the constitution of the USA was for USA citizens, but then I'm not from the USA and am watching all this from very far away.

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.

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.

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.

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.