1. You certainly can. You can use both, one, or neither of the adverbs "very" and "much":
It was understood.
It was much understood.
It was very understood.
It was very much understood.
I think that "well" works a little bit better than "much", but "much" is ok. Other adverbs can also be used to the same end: "greatly", "decidedly", "perfectly", "totally", "absolutely",...
2. All of those are used. Here are some other ways:
"the mere thought of speaking"
"just the thought of speaking"
"just the thought to speak"
You can also use "suggestion"
"Just the suggestion of speaking in public..."