Divine Divinity (DD) and Beyond Divinity (BD) are both single player only games (no online play). DD2 (in development) should have multiplayer, but there has been no information released about how it will be implemented.
BD is set 20 years after DD, and does continue with the plot (though it is more of an aside than a direct continuation). DD is a single character game (though you can have summoned or resurrected creatures follow you), while BD has 2 main characters and summoning dolls (which are controllable as party members, though not as strong as the main characters).
BD is separated into acts, while in DD most areas are available for the majority of the game, giving you a little more freedom. Actually, after act 1 BD does open up more.
If you had played DD first you would recognize a few references, characters and places in BD, but there is no need to have played it.
For the screen position, you should be able to start the game, and then use your monitor's controls to recentre the screen. Your monitor most likely stores settings for each resolution / refresh rate combination separately, so changing it in-game should not effect your desktop.