Yes you can, as modern video cards have flexible resolutions on dual or more monitors. Since you don't say if there is dual monitor linked images for games, what frame rates you require at what resolutions, it is up to you to experiment.
Have no idea what "Do they connect from the monitors or the graphics card?" means as the only reasonable answer is "both". If you don't have connection from computer to monitor, you get no image.
Using computers since 1962. Right now I am sitting in front of a 47" HDTV at 1600x1000, flanked by a 23 " monitor at 1920x1080 and a 19" HDTV/monitor at 1440x900, all doing MS FS2000 simulator, and it is fine. Main monitor shows out the front of plane and instruments, side screens show GPS, radio stack, trail plane view, top view.