I see someone answered our producing workers in a village hex already, so will move onto the other questions:
1) Is there any reason to have more than one Mech or Character in a battle? They don't add anything to the combat value generated, so can't see any reason for more than one Mech to be involved in a battle.
If there's no workers in the battle hex, there's no point to having a Character and a Mech in the same battle either as AFAIK.
As people have already stated - you can play one combat card per Mech and/or Character involved.
This is a pic from my last game - Polonia, despite having all 4 Mechs and Anna on the factory, could play up to 5 combat cards; they only had 3 cards at the time. I attacked with 3 Chrimean Mechs, I only had 2 combat cards however my faction ability meant I stole one of the Polonian combat cards meaning they could only play two and I could play three.
Nordic ended the game two rotations later after attacking my undefended territories...they won alas.