No federation. For either version of minecraft you have an account you register with microsoft, which among other things provides you with a UUID, allowing users to be identified and authenticated across different servers. The various UUID authentication utilities are not necessary to set up a server, they are just offered for security.
Minecraft servers store world data, NPC states, and player inventories. All server data is unique to that server (e.g players cannot take an inventory from one game server and transfer it to another, or access worlds from different servers)
There are two versions of Minecraft: Java (written in java, only available on PC) and Bedrock (available on all platforms, and also allow cross play between platforms). PC players generally prefer Java as it was the first version and supports modding. The server side of minecraft Java is also written in java. Not sure what the GPU part is referencing.
Minetest in particular is open source, by the fact that the underlying game engine can be modified to create new functionality not available in the base game. In regular Minecraft there is restriction on what exactly a Minecraft server can do and what client-side modifications can be made.
Griefing is basically trolling in game: destroying other player's buildings, repeatedly killing them in game, etc. Some server moderators will allow this, some don't.
Hope this helps :)