So if I were to be making a minigame system with each minigame being its own level. Can I make a server and a gamemode specifically for a level and keep on doing it for all other levels?
In short - no. 1 game - 1 server. But you might not need different servers to do what you want as GameState can do the work.
If you were to be making a minigame system that said system would be your server where players connect, have their stats/avatars displayed and choose their desired game.
From this point on you could:
- Keep the server the same, create different sessions for your games with different GameStates. After all you only need the rules to change which is done through the GameState.
- Make the player start another application connecting to another server which would mean every game is a separate project. This is usually done in Service type of architecture where the minigame system is not actually part of your games (and usually is not an Unreal project). (kind of like how Steam works)
Check this document: Game Mode and Game State | Unreal Engine Documentation
I hope this helps.
Happy coding 
