Here's my take on drywall vs skim vs full update.
Skimcoat
Skim coating over the plaster that is already cracking would not be a good idea. Even if you use a harder more durable mud or plaster, it will still most likely crack because of the age of your house, and the fact that your walls are already cracking (and will probably continue to do so). The other down side is the sanding mess.
I recently bought a condo that had nasty texture as well on the walls which I wanted to get rid of. I decided for the first room that I would use a heavy 60 grit paper to remove as much of the larger chunky texture as I could. I then skim coated with drywall mud to smooth out the walls. It took several coats to get perfectly smooth, and a whole lot of cleaning afterward. But, in my case, I know my drywall is sound and not cracking underneath, so I could reliable coat without having to worry about patching too much in the future.
Drywall
Using a thin drywall layer over the top may be a quicker and cheaper solution. This will eliminate the cracking issues and will give you as smooth a wall as you like, with little mess in comparison to skim coating the entire wall.
I would still use a 60 grit paper or paint scraper (if it will cut through your texture) and knock down as much of the heavy texture to allow the drywall to sit closer to the surface. This will help eliminate waviness in the wall where the texture might be outrageous (like it was in my house), and allow you to use a thinner drywall.
A possible major downside to this is electrical boxes? Maybe someone with more electrical knowledge can speak whether adding 1/2 inch thickness to a wall would cause issues with the electrical boxes being set further in? If so, again, I would sand and use 1/4 inch.
Full Update
If I was going to be living in this house for the rest of my life, I would consider a full update, especially if I was already going to be making changes to wiring.
This solution is costly, time consuming, and messsssy! But, the upside is that you can fix/update your electrical to be safer, and more suitable to modern appliances. You can also add low voltage through the house which (if you're a tech nerd like me) may be a nice plus. This will also give you perfectly smooth walls that won't crack and a feeling that your not hiding a mess in your walls.
Hope this is helpful!
You need to locate and identify the underlying structure, where and what. Only then can one determine the best attachment method and wall layout. Stairways typically have stringers under them running the length of the stairway run that you can connect to. But there are endless variations on stair construction, so only someone on site can determine this. There are various devices for locating underlying wood structure, their effectiveness varies by local conditions.
Stud framing is typically 40.5 cm spacing on center, so you may need two intermediate studs in addition to the end studs. You need solid blocking flat to the mounting face in order to mount plumbing fixtures. Some hardware needs to be framed into the wall, so you need to identify exactly what hardware is used in order to provide and locate any needed structure.
Unless you can provide all this information, no one can adequately tell what to do in enough detail to ensure proper construction.
Best Answer
Freestanding steel studs are fine (assuming they are anchored to a sill and top plate). Steel studs anchored to the furring strips are fine. Why wouldn't steel studs anchored to the furring strips, plaster and lath be fine? The only limitation would be if the lath and plaster had significant bowing or hollowing in spots that the new studs came in contact with (minor hollowing would not make much difference).
Also, as you install, you want to make sure that crumbling plaster does not get wedged in a way that prevents the studs from creating a smooth planar surface.
While plaster is not much of an insulator, you still have a bit of air trapped between the plaster and the brick in the furring strip troughs. Add high density batts or rigid foam between the steel studs to improve the R value.
If you are very concerned about insulation, wood studs are poorer transmitters of heat and should be considered. Also, creating a real thermal break by not having the inner wall directly abutting the outer wall would improve the situation. But this approach does eat up interior space.