Controlled sites won't receive the battleground keyword from
Suffered Much Loss, as they are no longer "on the adventure path."
You can discard
Gimli's Helm and then assign all threat wounds in that skirmish phase to him, preventing them all. If you don't discard the Helm, he can take at most one threat wound (assuming he hasn't been wounded yet that skirmish phase), and the rest cannot be assigned to him.
You're right. I went through the comprehensive rules (not that I don't trust you, but this seemed counter-intuitive) and found:
"If a character cannot take wounds, wounds
cannot be assigned to that character. However,
if a card prevents wounds, wounds may still be
assigned to that character"
(page 18)