1) 3.57945...MHz +- 10Hz. The color burst sets the sink's phase and the phase of the carrier riding on top of the luma signal sets the actual color. If there is phase jitter or noise between the burst and color carrier it can lead to the oscillations you are seeing.
2) I don't have a vector scope here so I don't know the scales being used
3) I can't duplicate the issue since I don't have a vectorscope here
4) If the input has a stable time base then turning off HSync processor should be OK. Need to test against all your sources.. Might also point to some kind of noise coupling in the system