Since I do not like to change the doors, because of plaster, etc. following question:
Is the door here in the photo (about 6 in the house) with cleaner-degreaser + 2-3 x sanding paintable? I would like to paint it in white.
Yes, if you sand, you don't need a degreaser as far as I know.
I have always gotten by without sanding in my recent painting activities. On one thing, I think it was plastic boards on a balcony, I needed extra primer. That's where I would double check what it's for and possibly use it in one coat before painting. I would work on the doors as well as frame with foam roller. If there are a lot of corners, pre-paint with a small brush and finish with a small roller.
Remember the rubber lips – if you want to do it right, change them after painting :)
If you are sanding, you could also glaze – that will preserve the grain.
Does the door have any real grain at all? Looks like the first layer is just glued on "foil" similar to a kitchen.
You could check this by looking at the corners at the top or bottom. Sometimes you can see that the whole thing is not real wood. So I'm not sure if you can really do yourself a favor by sanding it down.
When changing the door you would not necessarily have to change the frames. They are relatively neutral in color and with a white door maybe not all wrong? Everything white is then somehow also nix or does that deceive me? Couldn't you just foil a door like that, just like you foil a car?
It seems to me that the door shown is rather veneered. Actually, it wouldn't be much of a hassle to replace the door(s). If the trim is not glued in, the frame can even be removed without damage, even without damaging the plaster.
I wouldn't recommend painting it, because it will fail at the rebate and the corners. If you want to paint white, then paint the frames and door leaf.
First remove all fittings as far as possible (including the lock), then carefully remove dirt and grease with a gentle cleaning agent and sand the old paint with sandpaper (180 grit). Then clean again (dust-free) and fill any missing areas. If necessary, sand again and make it dust-free again. Prime and then apply a coat of varnish.
What I would do then is to change the handle set, but it's a matter of taste. You see, there is a lot of work to do.