Is it possible for the player to host their own server on their device? And can it still be playable when both players aren’t connected by Bluetooth or local wifi?

I can’t give you a direct answer, but there have been several questions asked about multiplayer games. Some of the answers were that there was a lot of lag time which made the game hard to play. You can search for multiplayer on the forum for more answers and others will jump in with their answers. Also, did you finally buy Codea or are you still on the fence from your previous post “Before I buy”.

@dave1707 Proud to say I bought it :)!!

When you bought the server nothing directly happens. All domains or Applications send a request to the server and display what the Server returns. Why do you need to buy a server, when you can install one on you local host?