If you don't want to spend money, I restored my plaster cornices by covering them in porridge, covered in clingfilm, for three days, which softened the many layers of paint enough to prise, scrape and flick it off the plaster surfaces underneath. No reason why this wouldnt also work on a plaster ceiling. Or you could use a chemical stripper. Or paint the black bits with a stain blocker, then paint the whole ceiling grey, then repaint in white. Just writing this has exhausted me. I'd phone a plasterer. They'll do it in half a day.

I love the panelling, picture rails and dado! They look like original features which are really sought after now. I wouldn’t remove them, it will be like ripping out the soul of your home. You can update them by using trendy colours such as grey, taupe and white. I think the taupe shades by F&B lend themselves beautifully to such features. Shades like Elephants Breath, Purbeck Stone or Skimming Stone. However your idea of grey would be lovely too. How about a mid grey on the panelling (not too dark), then a soft pale grey above. Or go all out white with the staircase in deepest charcoal grey? Here’s some ideas

I’ve never attempted that, but one of my mum’s neighbours house was painted red (the houses had lovely red brick so a bit of an awful thing to do) but new people moved in and painted it cream with black windows and black railings. It looks amazing. The row were Coronation Villas built in 1911.

Asbestos was used in textured ceiling finishes like Artex, and lead paint was used up to the 60s. I wouldn't worry if I was you. I shouldn't think it's dangerous.