Is the game for iPhone too or just iPad?
Yes it's on iPhone.
It's multiplayer in the sense that many people connect and play. (I don't have the game so I don't know if you interact with other players, but usually you can with these types of games).
So yes it does need to connect to a server. For example, if you build something and it takes a few hours in game, even if you turn off your iPad completely it would still be building since it's running on EA's server.
I have the game. I don't play it, but I do like the animation and the voices. But I just don't like the game play. I find it boring.