Yes when you register you have to wait for your beta key. Seems they give them out randomly. Any new keys given are not for the unlimited play though. They are now givibg keys for the free version which has limited access.
Yes there are quests and tasks to do, which is how you advance in the game, however seems many of the quests are not quite complete and mnay ppl have bugs that don't allow them to complete quests.
You move using the keys, but the screen and view control is with the mouse. there are MANY MANY bugs to be worked out before they can even think about releasing the game to the public. Graphics issues, freeze issues, lag, chat problems, friends list problems, login issues, and even weapons problems are only a few of the problems this game has.