If you equip a heavy trooper to your units, can they still use the "main" weapon on the base unit card? Where is this also in the RRG?

Yes. It's covered in the section that talks about choosing weapons during an attack. Only the heavy weapon trooper can use that heavy weapon, but he can use his "standard" rifle, and even grenades if you have that upgrade in lieu of his heavy weapon.

Also he can punch a guy in the face should that situation arise.

The rule is in several places, but at the very least its on RRG pg 44 under upgrades.

Hint, if upgrade models couldn't use the weapons off the base cards, the Personnel upgrade models wouldn't have any weapons at all.

1 hour ago, LunarSol said:

Also he can punch a guy in the face should that situation arise.

Oooo good catch.