So you’re saying that you want to split up your forum into multiple, entirely separate fora? If so, I’d think twice (or three times). If you originally had planned to make it one forum with categories, I assume that those categories do have something in common (they’re different aspects of the same thing) and in that case it’s clear that it should be one forum.
Yes, it’s possible. For discourse it makes no difference whatsoever whether it is running under a domain or a subdomain or whether there are a million other discourse instances in other subdomains. Domains are just a way of creating a human-friendly way of identifying the server on which discourse is running.
In principle, you could probably set up your instances as SSO clients of some SSO provider (or make one instance the SSO provider for the others), but as mentioned earlier, I think this will probably cause more problems than it solves.