Yeah, you'll have to patch the games. Just follow the instructions in the second post of this thread and you should be fine. Since you have an Nvidia GPU the problems should be minimal.
As far as your screen resolution is concerned, check out the Widescreen Gaming Forum. Their UniWS utility will work on KotOR 1, and there is a patcher by Squ1zZy for KotOR 2. Don't forget the HUD files for both games.
"Mind your wants, 'cause someone wants your mind."