Clarification re: Nazgul and characters, can you attack them as a single?
Combat can only occur between 2 armies. Companions or minions by themselves do not form an army. They are only part of an army if there are friendly army units in the same region.
They cannot be killed when they are in a region without friendly army units. (Except when specifically mentioned on a card, like the Ent-cards kill Saruman)
They are perfectly fine walking (or flying) about in the same region as characters or armies of the opposing side.

The question I have then, say the Shadow player flies their Nazgul to adjacent the current known location of the ringbearers, but then Free Peoples player musters and moves some armies:
Does this result in combat? The Nazgul having no combat strength, it instantly dying?

No. Nothing happens. There are no Shadow units in the region, so the Nazgul are not part of an army.