It runs for another 9 months or so I think so that all dates get a turn.
It is account-based. Even sharing a DS and PC you'd be able to have an hour each with seperate accounts.
You do need a DS and a PC to use the Dream World, however you do not need them simultaneously. The DS is used for Sending Pokémon to the Dream World, which then you can access on a computer over the internet on an account linked to your game, and then afterward you use the DS again to recieve the Pokémon back from the Dream World.
Well that wouldn't be good for me... since I have no PC access. So way to go Game Freak and Nintendo on this one. Talk about leaving a lot of people out this time around.
I might be able to convince my cousin to let me use it when I come over every now and then, but other than that I'd be screwed. Since all I have access to other than that are library computers and they don't run on the same kind of wireless.