In removing a layer of painted wallpaper I managed to rip through the paint layer beneath and exposed some drywall as per photos. There’s also quite a lot of screw and nail holes which have have some quick filler for. I intend to repaint the white wall and I am wondering if using standard plaster wall filler would be the right thing to go over the torn patches.
Before painting the wall you need to wash it to remove any trace of oils, grease or dirt that would prevent the new paint from sticking. Let it dry.
Use a spatula to remove all the paint that isn't attached to the wall. Look for cracks or paint flaking off, bubbles, etc. You can rake a wide spatula everywhere, that will also take out any debris caught in the previous layer of paint that would otherwise make little warts.
Sand the area you want to fix lightly to remove any bumps or stuff sticking out. If some of the drywall cardboard sticks out you can carefully cut it. The goal is not to have anything that will poke through the mud.
Apply some drywall mud to cover the damaged patches. For tiny holes like screws or nails you can make it flush with the old paint, but for large areas like in the picture you won't be able to, so it is better to apply mud over a larger area. Then let it dry, and sand it smooth.
Did you save the bits that were ripped out?
That wall looks like a textured finish, so you'd do far better to patch it back with PVA like a jigsaw, then deal with the joins, than try to match the finish with new plaster.
Especially on a 'satin' [slightly shiny] paint finish, your eye will be drawn to it all the time. It will stick out like a sore thumb.
Here is an example, originally caused by water damage. Not only a textured surface, but a textured glaze wash, clear brown over yellow, which I absolutely did not want to do over.
The area you can see is about 6"x4", lit from above to emphasise the join. From more than about a foot away you cannot see this at all in normal light. (I had to put my finger on it so I could find it with the camera;)
If you're going to repaint anyway, you could just rub a tiny amount of all-purpose wall filler in this join with a finger, before you paint. It will completely vanish.
I found another bit from a different wall, also previously water-damaged. This is a smaller area than above, maybe 2"x1" & has been repainted. The overall damaged/repaired area is much larger & I knew I'd missed a bit when I rubbed in the filler, so a mere 10-minute search across the area & I eventually found it ;) This time lit from below so you can see it more. It did take me several minutes to find it waving a torch [flashlight] at different angles & I already knew roughly where it was.
Put some oil-based primer (like Killz - rattle can is great for this) over the torn spots. Let it dry, then put on a coat (or 2) of drywall compound to make those areas flush with the surrounding wall (feathering over a larger area as needed). Prime and paint as usual.
The oil-based primer prevents the paper from bubbling when you put the compound on (the paper will absorb the moisture from the compound).