We know that the authority the Enterprise answers to is a "combined service
That depends on your point of view concerning changed premises. It's obvious that early TOS went through different writers' interpretations of the Enterprise's governing body before the Federation/Starfleet was settled on. That doesn't mean that these separate agencies actually existed.
We know that there are "12 like the Enterprise" in the fleet
We know that Star Central and UESPA are somehow related
Again, see above concerning changed premises.
We know that the Enterprise frequently gets referred to as an Earth ship
Again, I tend to chalk that up to a changed premise. Was the Earth thing spoken more in the first season and the Federation spoken more in the 2nd and 3rd?
We know there is at least one ship crewed solely by Vulcans (the Intrepid) - do we actually know she's the same type as the Enterprise?
All we know is she had a crew of 400 (and since Spock stated this, it's probably accurate even though an exact even number seems odd for a crew count), and her registry number was possibly 1831.
We have seen several other members of the class that the Enterprise belongs to, and seen reference to registry numbers (but no names) of other ships
Solely from information from TOS, we know:
Constellation NCC-1017 (Constitution class)
Republic (NCC-) 1371
NCC-1831 (possibly the Intrepid)
Lexington (Constitution class)
Hood (Constitution class)
Potemkin (Constitution class)
Excalibur (Constitution class)
Exeter (Constitution class)
Defiant (Constitution class)
Older Starfleet vessels:
It appears different ships have different insignia on their uniforms but share the same rank structure