Yes! Awesome maps and campaign dlc! You get to play as Nightwing and Robin! The dlc campaign is pretty cool! Batman has been captured and play as Robin to save him! Arkham City was favorite of the three. Awesome story! Game of the year edition is a must have! Make sure you preorder the next Batman, Arkham Knight, it's going to be epic!
I don't want to make guarantees because I haven't actually tried, but I see no reason why the first disk would be different than the original. The only difference should be the second disk and it is all dlc, so in theory, the dlc should download to your console and connect to the game itself, not the disk. Again, I am not certain, that is just my theory.
Basically. You are free to roam the entire world from the beginning of the game, and there are enemies and events across the map that you can do anytime. A few buildings cannot be entered unless you progress through the campaign, but you can go anywhere in Gotham City at any time. Hope this helps, and this is really an excellent game
Absolutely not, Batman: Arkham City is a pick up and play type of game. The only real perk of having an online account is you have the opportunity to get a high score in some of the combat challenges (which is no real reward). This game ships with two disks one for add-on-content and the other is the original game disk. Neither require an internet connection of any type