“And how can it behave like a wave and pass through a vacuum, when all other waves require a medium to propagate?” Um, maybe the ‘vacuum’ is not empty. Maybe the vacuum is an energy field (called the zero point field) and the wave propagates through the medium of the zero point field of energy. Perhaps there is an infinite field of point/moment loci through which the photon wave propagates.
You're onto something there. As some would say, just because you can't see it, doesn't mean it isn't there. The so-called "vacuum" appears empty to us because we can't detect anything in it. There is a bunch of dark matter in the Universe hiding from us. It fills the so-called "vacuum" with energy fields and light propagates through that medium. It also binds celestial bodies together with electro-magnetic energy. Someday scientists will be able to readily detect dark matter and how it exists within the "vacuum" of space.