They are an active regiment in the British Army. You’re probably confusing them with the Beefeaters, who wear an entirely different uniform, and are mostly ex-service persons.

I believe the king's guard only recruits from enlisted veterans. They also have to have been deployed to an active warzone. In those terms, it's both quite relaxed and an important position. The pomp and ceremony that visitors see is only a small part of their job.

Not quite, Royal Guards typically know what they were getting into - it's a little more involved than just joining the military and being tricked into the position.