This is a kind of risky subject because I don't want too many assumptions to be made, and I'm sure I've made assumptions myself about the inspirations I draw on. I've tried to make all the CLOK cultures be unqiue, even when they're based on real-world ones. That said, I'll offer some inspirations the CLOK cultures have had.
Tatlhuecan has some
loose parallels to the Aztecs and similar ancient mesoamerican cultures.
Nuum has some
loose parallels to ancient Egypt.
Tol Rhun pretty unique. I can't think of any real-world parallels.
Ivial is, ehhh, kind of a mashup of Ancient Rome and the idealized Arthurian society of legend, with its own further quirks and unique points. Their language is obviously strongly based on Italian. Honestly, don't make any assumptions on this one - it's mostly unique at this point, with just a few inspirations from those cultures.
As Lysse said, Faewyr have a strong Scandian influence. I shamelessly pull from various different but similar real-world cultures and combine them as I like.
Giganti are pretty unique, but have some small Scandian influence as well (mostly their language and script).
Hillfolk are kind of like frontiersy colonial-era American independents, I guess. They prefer keeping things small, simple, and independent, away from the interference of others.
Parrens are, hmmm ... pretty unique. Kind of hard to nail down. There's some mixture of the stereotypical easygoing Pacific Islander culture and the Age of Sail Caribbean stuff. Their culture isn't very strongly developed yet, to be honest.
When I think of Grum, the first thing that currently comes to mind right now is that movie "
Hugo." All the clockwork and gears and fun stuff like that, and that whole "feel" the movie has.
Rithiel can comment on the Fasa if she likes.