[Sideband]

That is a very typical frame fault.. a 'partial' frame collapse. As HKS says, it will undoubtedly be caused by leaky wax capacitors in the frame output and oscillator stage. These will all need changing but while you are learning, change one at a time so you can see the effect.

No doubt the poor volume will be caused by the same problem. All the leaky waxies will eventually need to be changed. Don't leave the set running for too long since other components (like output transformers and frame output transformers) can fail while all the leaky waxies are still in place and these items are far more difficult to source for the sake of a few cheap capacitors.

It's quite safe to measure the boost HT with a standard meter. Use the 750 or 1000V range and make sure you are using good, well-insulated test prods.