Does she know that you (presumably) don't believe in supernatural things?

Yes.

Does she know why?

She might have a vague idea, but I've never gone over it in detail.

How do you explain (to yourself) her stories about seeing spirits.

Mostly, they sound like hypnagogic/hypnapompic hallucinations, also called "waking dreams" - the same kind of thing that inspires "I was abducted by aliens" experiences. For example, my aunt tells a story of seeing a red traffic light over her bed one morning when she woke up: she thought "The light is red, I should stay home" and went back to sleep rather than get up and try to be on time. My girlfriend also frequently complains of insomnia and often texts me in the middle of the night.

Those seem to be a lot more serious than simple beliefs in absurd things like "healing powers" (or astrology, etc). Do you really believe she's not crazy? Is she making it up? (If so, why?) Using drugs? Believes they're there but doesn't actually see them, just "senses" them or something?

Well, she doesn't act crazy, and I'm not qualified to give a psychiatric diagnosis.