I've been curious about some of these things too. My employer is HQ'd in CA, which forbids non-compete clauses in contracts, but I work out of the WA office, where non-compete clauses are ok, and my contract has one. I don't know of any former employees sued so I'm not really concerned about it but I always wonder if it would hold up in court...
My company's headquarters are registered in Texas, but we have an office in CA that is doing hiring for that office.
Same as above, but hiring someone residing in CA to move to Texas.
Same as above, but hiring someone residing in CA to remote work (in CA or wherever they please).
Then, all three cases, but with a company headquartered Int'l.