Questions in title. I haven't tested directly, but in my experience, it feels like the answers are "no" and "yes", respectively.

(3) Do imps, hellhounds, etc. receive Commander bonuses too? Or are only units present at the beginning of the battle eligible?

That's interesting. I thought he was somewhat strong, but I assumed that it was mostly due to equipment bonuses.

Interesting. So when facing an enemy commander, if you kill him all the rest of the army will have lower (normal) stats? That might change my strategy in a few battles... like fighting a Tactician with a bunch of centaurs.