No, the chests will not respawn. The one next to your bed (to the right as you enter the Cistern from the Ragged Flagon) is definitely safe.

Does the thieves guild vault fill up?

One of the things that aggravated me the most was that although the thieves guild becomes rich, the vault room never fills back up. ... Once you complete that mission your thieves guild will "level up". You do not need to complete the jobs in Riften because the thieves guild already has presence in Riften.

How much money does the Thieves Guild give you?

You can make upwards of 20k~ a day maxing your fence limit for the day.