I want to use it to run several sites which appear completely separate. Can I set up another domain (B) which will access the same product database but appear to be completely separate from Domain (A) and at the same time limit Domain (B) in terms of categories with Domain (B) showing only categories A, C, & G?
Not by default on the same DB
There is a 3rd party(Not By the ZenCart developers) for Multi Site module and a thread also on this site for it but it appears that the author is not active any more - - others might be able to assist?

Is there a limit to the number of domains I can attach this way?
Seperate Domains - - You need to ask your host the limits
BUT I can state that if you require SSL for secure payment processing you either need discrete accounts each with a dedicated IP and SSL Cert

Can I apply different Templates for STYLE and layout of each site or would they all have to be the same?
See above for multisite module