1) BF3 = Squad-based team tactics mixed with FPS play and vehicle driving/flying.
2) The Campaign is allegedly good according to which reviewer you read; some will compare it to every modern day shooter in that it's the U.S. and/or Coalition Forces stopping a nefarious plot set forth by those damn dirty Terrorists.
Others will dig the story for it's depiction of war in the possible near future; no zombies, no aliens, no robots versus humans... just a man, his gun and his tank/plane/personnel carrier if need be.
3) The Co-Op I believe is Local On-Line/Offline and you could also take it online if you'd like.
4) As for just playing online, the premise is the same: You want to get a high score by the end of the round, with unlocks to earn as you progress in rank... the same as COD.
The difference is, you're rewarded moreso for helping your squadmates out and generally doing things as part of a team.
Also, the maps are bigger that COD and depending on which game mode you play in online, they could be damn near huge.