As to why, basically anyone is allowed to run their own copy of lemmy and some people actually enjoy doing it. There is more nuance of course. For instance, the owner can block other people's instances for whatever reason so no one on their instance sees content from the other instance and people from the other instance can't comment or vote in their communities.
There are definitely pros and cons to this approach, but the cool thing about it is the whole thing is back in the hands of real people and not owned by a bunch of investors.
This is what you want, op. Realistically, covering a space like this means running some cable and using it to connect everything. You'll have one router that connects to the fiber gateway then probably two or more access points connected to the router, those can be old routers if you have one or more laying around, or just WAPs (wireless access points).