The colored lines are normal, they are the times when cathodes are being measured to compensate for wear and get good color balance until end of tube lifetime without any further adjustments.

That ringing is "normal" in the sense that every display has it, but the extent to which it is supressed will vary. There's an interplay between deflection coil + flyback + deflection capacitors that causes it. Perhaps the flyback has been replaced and isn't an exact match to what was there before or maybe this was like it always...

The last thing is a result of AC coupled video stage somewhere. It can be reduced by having fresh capacitors if they're electrolythic kind.