Board Game Arena

Could someone please tell me the benefits of a premium membership? Is there a difference, when playing a game, between Non-premium and premium? Are all games "premium"? and what does that actually mean?

This should answer most of your questions:
https://boardgamearena.com/premium?src=globalmenu

There is no difference when actually playing games (despite some players saying BGA fixes it for premium players to get better dice rolls etc!) But it allows you to start tables of premium games which are marked with the little meeple symbol

Premium also allows you to play people on the same WiFi as yourself which you normally can't

Yeah the thing really great is that for some games like Carcassonne, you can choose yourself with which extensions you want to use. It's complicated to find tables which correspond exactly at what you want! But for most of the games there isn't a real difference i guess