Companion skills

[Charlemagne]

Do companions use their skills without you ordering them? I find ordering skills too cumbersome, usually the battle is over before I need anything and besides they always run off to engage the enemy it would be hard to micromanage them. I haven't even bothered in trying to learn what they do :-P
But my question is because I wonder if investing in those perks that affect their skills will help anyway, or using consumables that affect their skills.

[Charlemagne]

Another related question, I have changed their weapons to better ones, but in the special skills description it mentions that they use their *specific original weapon* to do stuff, do they lose the skill if they change weapons?