Yes, just connect both monitors to the DVI slots.
VGA cables are not as good quality. There's a noticeable difference. Basically, DVI cables carry a digital signal, and VGA cables carry an analog signal. Digital is better basically, you want a DVI cable for the best quality.
While you're playing a game, your cursor is "trapped" inside the game so to speak. So without minimizing the game you wouldn't be able to use other programs, I've tried before.
When most programs are open though, you can just keep moving your mouse and the cursor will reappear on the next monitor.