"Actors perform in theaters."
Translation:Aktoroj rolas en teatroj.
No; an aktisto is an official who edits and preserves official acts.
There is not verb "akti" (though perhaps it could mean "to be an act"), and -isto compounds are usually formed from verbs.
Since there is a verb "aktori", you could perhaps use aktoristo if you wanted to emphasise someone who professionally acts.
I suppose, but actors are not only found in theaters (movies sets, TV sets, acting classes —both as students and instructors—, etc).
Conversely, theaters are not uniquely for actors: directors, set designers, property masters, lighting designers and sound engineers, dressers and make up artists, ushers and box-office employees, management…, not to forget the cleaning crew ☺
In addition, I've seen theaters hosting dance or music shows, so no actors in this case.