All video cards since x800 and 6800 series had dual-link to my info. So your 9800GT should support 120Hz when you use a Dual-Link cable (thick ones) but yes, your GPU will most likely not keep up as 120Hz cuts your FPS in half.
No and those TVs aren't actually 240 frames per second. The signals are 60hz but there is a small GPU inside the TV which takes the 60 FPS signal and creates intermediate frames with it. So even a single link cable would work.
Also 240hz TV for computer is bleh because to create those extra frames you get like 2 full seconds worth of input lag.
Displayport can technically do 240hz but what game are you playing? Some old games maybe. Or the low end ones like Modern Warfare 2 or L4D2. Otherwise 240 FPS is hard to reach.
I am gaming on 2560*1600 and I can't even max settings witout going under 60FPS for games like Bad Company 2. Maybe in the future we have crazy video cards that can do 2560*1600 at 120hz. Honestly 120hz isn't necessary.