Can the Samsung Galaxy Tab run Facebook games and applications? Can I open any Facebook games/applications on the Samsung galaxy tab? Games/applications like farm villi, Poker etc will work properly in the tab.
The builtin browser will probably show you a touch-optimized version of Facebook. You can try to get rid of it by changing the user agent string. See this question for more info on that.

Edit: Also, if the games require click-and-drag, this won't work on a touch screen.