Is Modern Warfare 3 still playable online?

Yes. Activision's official matchmaking for the 2011 game is effectively empty, which is why most search results say the game is dead — but that only describes the official service. Community dedicated servers running the Plutonium client are active every day, and this page shows how many players are on ours right now.

Because the official ones effectively are. Those pages are describing Activision's matchmaking, which has almost nobody on it. They were written without reference to the community clients that kept the game playable, so the answer they give is accurate about the wrong thing.

It is a community client that has been running for years, it is free, and it requires a legitimate copy of the game — it does not distribute game files. One practical point worth knowing: the original multiplayer used peer-to-peer lobbies, which is what made it a target for exploits and a large part of why people stopped playing. Plutonium play happens on dedicated servers instead. For anything about the client itself, their documentation is the authority, not us.

No, but you do need to own it. Plutonium is a client for a game you already have; neither they nor we hand out game files.

Yes. Every server is free, with no whitelist and no queue. There is an optional VIP tier that covers hosting and sells no gameplay advantage.

Standard multiplayer — Team Deathmatch, Domination, Search & Destroy and the rest — plus Spec Ops Survival co-op, which the Plutonium client does not officially support and which runs here through a server-side recreation.