To the first part of the question about the code:
You can enter the code in the Uplay client and download the whole game online. I always do it that way and it's faster with 1Gbit fibre than from disc. Another advantage: the updates are already there. I can't say whether this also works from Asia, the codes can have regional restrictions.

To the second part of the question regarding different DLC:
When you start the multiplayer game, you select the active DLCs in the game round. Only those that are active with all participating players are available for selection. If you don't have any common DLCs, then you only play with the basic game.