In GMT you were able to send items straight to your condo to use to be sent into a vault.Will there be a system just like this?
The only point of the vault system was to store items that you didn't have space for in your inventory. Since TU no longer has an inventory cap, adding a vault system similar to that in GMT would be pointless.
Yup, what CarbonCopyCat said. Your new "vault" is the furniture tab on the hot bar. The stash command is the same as the vault command.