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Once I've done the first mission can I kill them all? If not how do I finish the join the thieves guild quest?

You need to raid the rooms in the back of their hideout. They have VERY strong enchantments and locks, so you need good environment magic or skills or scrolls. You should get a really badass sword and shield and a wand and scroll that are okay. Sadly, you need to bring these back to the mysterious man. That ought to finish the quest.

The cells or the living quarters and I assume I can kill them?

No, if memory serves right, there ought to be two big doors in the way back that need disarming/unlocking. Inside is a room with some really good stuff you have to steal. But, I suppose you don't REALLY need the Theives after their mission. Just keep a save before you kill them, in case they are important in some way I don't remember.