I've never played an MMO, and the only reason I am looking at this one is because I love TES so much.

Can you just go off and adventure at random on your own like in any other TES game? Will there be a lot of dungeons to explore that you do not need to be doing a quest to clear?

Probably. From the sound of it they really want to preserve that aspect about dungeons. Supposedly raids are pretty flexible for how many people you can take and be effective, too.