1. Multiplayer is free, you just have to set up a Windows Live account.
2. BFM does not have any Halo 2 servers at this time. It does not look like we will be getting one in the near future as well.
3. As far as I know, Halo 2 uses the same physics as Halo 1, jus tthe graphics are better and more detailed.
4. I have never played CoD, and I have never played Halo 2 multiplayer (because I can't connect to Windows Live for some reason), so I can't help you there.