For stills, the shutter opening needs to be twice as long as the reciprocal of the frame rate, so 1/15th second should work (where the frame rate is 30fps - North America and other parts where 60Hz electicity is used.) This allows two full frames, and should eliminate the black bar. If it's not enough, you may have to double the time again. I don't have experience with doing this on progressive scan signals, but for interlaced TV, this has worked.
Focus is a problem, if you are trying to get a full screen image on a still. Digital cameras will give you a very nice image of the shadow mask on a crt set, or the pixels on LCD. You do need to defocus a bit. TV images are not really sharp anyway - as you will find if taking a still frame from any video.
For the color problem, you will have to adjust the color on the TV down considerably from the way it is normally set, and lower the contrast as well. I can hardly stand to watch other peoples' TVs, or the ones in store demos, because they always have the color an contrast set way too high. (used to do TV repair work, and would set them up correctly when they left the shop - if I saw the same set again, it had the color and contrast cranked up)
To shoot video of video, without the black bar moving through the screen, you will need a very complicated setup to sync the signals, or use a slower frame rate. 15fps has worked for me. If you don't have that available, I think you're out of luck.