Yes, muna can do a lot of things. What kind of hugareida did you think first kill muna gave? The answer is that it doesn't give one (depending on circumstance, of course. If you burn someone to death that's going to give you a fire hugareida).
Typically, first kill muna gives you a Twist or something (You don't know what Twists are, get one to find out)
Absolutely. An example of which would be the Mead of Poetry or water from Mimir's Well. Now, both of those thing's aren't exactly very common (at all) but lesser things exist.