Can you play Warzone 2 without Modern Warfare 2. As confirmed when Modern Warfare 2 was originally announced, Warzone 2.0 is "the new, free-to-play battle royale Warzone," so although it's built on the same technology that's powering MW2 you won't need to purchase that full-price release to get access to it.
Movement has been changed a lot between Warzone 1 and 2 whereas in the original you could run, dodge, and slide-cancel ultra quickly, in the sequel, you're much slower and more cumbersome, which makes reacting to incoming fire and getting into cover a lot harder. There's also the issue with time-to-kill or TTK.