Lapistia

Can a religious skill be chosen like a regular skill, or are there any special requirements (besides those mentioned)?

Well, for example, a non-human cannot be a priest, because this is a skill of the Kalevrit faith, which implies the need to eliminate all non-humans.
There may be other such moments, but it will be easier if you name which combination of race/religion you like, and I will tell you if it is acceptable.

Is a pistol specifically required, or will other firearms work?

Yes, only a pistol is needed.