Are walls plaster? Go buy a bucket of drywall compound and a 10 or 12 inch drywall knife, and try a sample area. Don't try to build up thickness, just see if you can get a thin coating that fills the texture. You'll probably have to thin the compound with a little water and stir to make it more buttery and able to apply with a feather edge. If you do it right, there will be very little sanding needed afterwards. Take a look at the results of your sample, see if you like it, then decide if you want to do it or get a pro to finish. Around here, finding someone willing to do it is 90% of the battle.

You could try using a good quality self leveling paint.

Looks like textured plaster to me. Its supposed to look like that. However those first pictures look like the paint was a shiny type, like semi gloss. Please do not put that on that type of walls. Eggshell finish, or matte finish would be the best.

Paint will not make it smooth; you need to skim coat it. You should try a sample to be sure it will adhere well.

My both set of grandparents had plaster walls. One home from 1930's one from late 1900 or so, yours looks more like the 1900 home though. Both had textures similar to yours. You probably need to use a oil base primer over that paint whether you just paint with acrylic or try skim coating for adhesion, good chance it's oil based paint. Also, this older paint could contain lead, most likely does if an older home. I would worry about breathing in dust from lead paint and stop the sanding.

It might be a good idea for you to read up on plaster walls and how to work with them on the web. Lots of info out there.

The walls would look less bumpy with a paint less shiny.

Your efforts are, unfortunately, misplaced. As others have pointed out, what you consider a defect is simply a feature of the walls. What I will add is that asbestos was sometimes added to plaster walls, and continuing to sand them down like this could contaminate your house and cause health risks. You can't know without testing, but, in any case, I suggest you abandon this approach and deal with the walls using one of the simpler techniques described above.

You also have done some patches that are not done in a texture to match the rest, and once you have primed and painted, those patches are going to stick out like sore thumbs because they are smooth.