"Fast shot" and "Bonus Rate of Fire" perks stack, so you will have -2 AP for shooting.
"Living Anatomy" perk adds 5 damage only after all damage calculation. No matter how much damage you made, it'll always add 5, even if you hit for no damage, you'll hit for 5 damage then, if you critically bursted your target on 300 damage, with this perk you'll deal 305 damage.
Mercs do train, they must kill mobs for this, and of couse they doing it very very very very very very slow.
You can't give armor to your mercs/slaves, they will simply carry it.
They will use weapon you give them, but some skins don't have weapon skins, so every slave can't use all BGs, different peasant skins can use only 2-3 weapons.