Can i play minecraft offline?

Yes, you can go on single player mode and play survival or creative.

Yes you can, however you obviously won't be able to play on multiplayer mode! But you can play on your single player worlds ^.^

Yes, you can't log on to servers while in offline mode however.

Yes but with the new 1.6 launcher you have to have logged in online at least once and if you log out of the launcher you will need to re-connect to the internet to log in as yourself