Yes, Call of Duty: Modern Warfare 3 has full cross-platform support. This means that you can squad up with players on any console PlayStation, Xbox, or PC and enter the battlefield together. This is true for any online mode in the game.
Unlike some other Call of Duty titles, namely Warzone and Black Ops Cold War, Vanguard does not ask for a lot in terms of storage space around 50 GB including the campaign mode, as I said before. And, if you are a fan of multiplayer, you will not be disappointed since it also supports crossplay.