What are the legal requirements to be a "crewmember"?
I'll take a stab at this one, though I can't guarantee the correctness of my interpretation (the regs don't seem exactly clear on the subject - at least not to me, so there's a lot more "inference" here than I'd normally be comfortable with).

In most cases under Part 91 the only requirement to be a "crewmember" is that the pilot in command says you're a crewmember -- i.e. the PIC determines that a person is qualified to perform a specific duty and designates them to perform it.
In the absence of anything more specific this is the only requirement I can turn up (and it's an inferred requirement - I didn't find anything specifically stating this, but 91.533 regarding flight attendants strongly implies that it's the correct interpretation. There's also a counsel opinion from 2008 - the Schehr letter which talks a little about who is a "crewmember" for purposes of riding in jumpseats that are placarded "For Crew Use Only". That interpretation is based on Part 135, but could be logically extended to Part 91 (and possibly some 121) operations too).



There are frequently more specific requirements though, particularly for positions that are important to flight operations. For example if you buy yourself a nice shiny Lockheed Electra to duplicate Amelia Earhart's trip under Part 91 rules you still cannot simply designate someone off the street to be the Flight Navigator: the FAA has specific requirements for Flight Navigator certification, and someone acting as the flight navigator would need to meet those requirements.

There are also more stringent requirements that are imposed for Part 121 and 135 operators. For example they can't simply designate a person as a flight attendant based on the PIC's determination that they are qualified: There are requirements for filling that crew position which must be met (FAR 121.421 &amp; FAR 135.295 respectively, and possibly other regulations).