Yeah, there's a story somewhere there that hasn't been told 100% about how Snoke, Ren, Hux etc. sort of overthrew the First Order's original leadership, mainly composed of aging Imperial officers (Sloane, Armitage etc.) and made it their own thing, although there are still some old Imperials still in it's ranks-Captain Canady, the Dreadnought captain, for instance (Who thinks Hux made a blunder by not scrambling the TIEs earlier to take out Poe's ship).
About the Rey's third lesson scene, one thing I liked a lot is that Luke's laugh sounds very "Jokery" when he says "I'm sorry, you just ran so fast!"