This problem needs to be fixed before going any further. When you launch the game, do you get a message that you are not connected to the Origin servers? This means you are either not connected to the internet or there is another problem preventing your PC or console from logging in to the Dragon Age Servers.
You might want to go online occasionally when you play so that the game can send your progress to the Keep and update your Inquisition world state, but that's entirely up to you. or if you want to play multiplayer :) For single player gameplay, it is not necessary once you import your world state. Note: The only time you have to be connected to the internet for Dragon Age: Inquisition game play is when you first start a game and want to import a world state from the Keep.