Unless the emergency exit is manned by the crew, they need a passenger there who can open the hatch if needed.
Normally this isn't a problem, as someone usually prefers that seat due to the extra legroom. If there aren't many passengers on the flight, and nobody has booked that seat in advance they might assign that seat early in the process so that someone who isn't fit to sit there can have someone else take their place.
A few times, on smaller flights with free seating, I've been asked if I can man the emergency exit. I normally sit far forward on these flights, but I don't care hard enough, so I'm happy to oblige.
As for who can sit there, it's not a particularly high bar: any adult who is reasonably fit who is comfortable with being responsible for the emergency exit.
Source: Partially through observation, plus I had a chat with a stewardess on the topic not that long ago.
Amount of international flights I've been on so far this year: 20ish, I think
Amount if times someone cared about my signature: 0
Only time there has been extra hazzle was when the airline questioned my C1/D visa as I didn't work for an airline. Took them a while to realize that ships also travel internationally.
Oh, and there was this time I had one of those DE9-RJ45 console cables in my backpack, and I had to explain what it was for during a routine inspection.