Train fight = From Russia with Love

Oh and the institute in the Alps (really everything in the Alps) = On Her Majesty's Secret Service.

After a first watch, my initial takeaway is all the fan service they did throughout the movie, which totally takes you out of the movie, in parts. By my count:
Rolls Royce = Goldfinger
Volcano-like lair = You Only Live Twice
Mr. Hinks = Jaws
Shooting at a mirror/bulletproof glass = The Man With the Golden Gun
Pre-credits…