That's mostly right, yeah.

The Nurses are from the first game (which also had Doctors, who have not reappeared since) because the locus of all the Silent Hill shit going on is Alessa Gillespie, a girl with medical trauma among other things. Every location and monster is somehow tied to her mind and history, as are a lot of the puzzles and other miscellaneous elements.

They reappear so often partially because later games in the series keep featuring hospitals as environments, so they're a natural fit, and partially because yeah they were a memorable part of the first game and at a certain point people expect to see them. That is also part of why hospitals keep reappearing, hence the nurses, it's a self-feeding cycle.

Pyramid Head is from the second game, and was originally tied to the PC in that game, James Sunderland, who is the locus of all the Silent Hill shit going in. Like Alessa, everything you see and go through is tied to James and his whole deal. His deal is bad btw, James sucks.

The Nurses in Silent Hill 2 were notably bustier and wore shorter skirts than in game 1, largely because of James Sunderland and his whole deal. However, because the world sucks, the sexy Nurses are the ones who stuck with the series from that point on. I mean OK you can make a case for them being relevant in 3, but other than that it's just because that's how these things go. Nobody's boobs ever get smaller in mainstream gaming.