[old_tv_nut]

1) It seems odd that the color oscillator beat frequency should be affected by fine tuning, but is very normal that when adjusted using one source it will be different with another source. It depends on whether the sources are close in color subcarrier frequency or not.

2) At the horizontal sweep rate you are using on your scope, adjust the 3.58 traps for minimum "fuzz" (trace thickness), which is caused by residual 3.58 MHz at the output of the demodulators. You may also be able to see the 3.58 MHz in the picture as a fine, moving dot pattern.