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"People will have heard their names and respected what they did" is past-in-the-future (future perfect tense), meaning that, in the future, people will look back on a past time (relative to the future) and respect what they did. "People must have heard their names and respected what they did" is (I believe) a present perfect tense with modal "must," it means that, in the present, we are considering that is must be the case that people heard their names (in the past) and respected what they did.

In the first sentence, dare is NOT used as a modal verb, it has the meaning of essentially "to coerce someone to do something by insinuating that they are weak if they don't." "He dared me to ask" means he (someone else) pressured me into asking a third person (probably the boss) for a salary increase. "He dared (to) ask me" is a modal use I believe, it means he surprisingly showed the initiative to ask me (the boss) for a salary increase.

"I daren't ask him how she is because they might have split up" is definitely a modal use, it means "I cannot bear/manage to ask him." Note that dare isn't really used in this way in American English, it sounds very British to my ears. But obviously fine if that's what you're going for.