Does the 6th tier Archmage path ability Sanctum come with food like mage's magnificent mansion? And would it just refill each day?
Is it possible to increase the size of the Sanctum?
Would it be safe to assume it would come with some sort of magic lab suitable for making magic items?
By concentrating for 1 minute without interruption, you conjure the door to your own personal sanctum, similar to mage's magnificent mansion, but with the following differences.
The given differences are the only differences, so yes there is food. As written it does not refill, but IMHO it would be reasonable to ask the GM to tweak that; it may simply be an authorial oversight.
I see no way to increase the size except to gain tiers.
You don't need a special magic lab to make magic items, just a quiet place to work---you can even get some work done on them on the road while adventuring. So it's safe to assume there are suitable places within the Sanctum unless you go out of your way to design it otherwise.