It's important to mention that while Black Ops 1 is still playable in 2024, the player population may have decreased compared to its prime years after release. This means that finding multiplayer matches might take longer or result in fewer opponents.
Yes, you can play both the campaign mode and multiplayer mode in Call of Duty: Modern Warfare 3 offline. The campaign mode can be played in its entirety in offline mode, and a Private Multiplayer mode allows you to access all of the maps and modes present in Multiplayer.