You do keep your AAs and any innate abilities (increased strength, hp, dps etc) still work at level 1, casting abilities i think have level requirements somewhere in the 50s area but that all depends on what AA you're using.
It seems that most innate combat enhancements like Spell Casting Fury, Combat Fury, and Critical Affliction don't start working until or near 50 (I had a spell crit when I was 48, and I thought it was a little weird, as I thought I wouldn't see one until 50). But (on my ranger at least) I noticed that things like Entrap and Innate Camo worked from level 1.
I'd like to think things like CS/CA are working at level 1, but I'm happy with Entrap and IC, lol.
I guess , for the most part you just have to test them once you de-level to find out which ones work for what classes.