Dampness in the basement on the floor slab and walls

I’m getting back to you faster than expected. I have now cleared out the first room and didn’t remember that the floor no longer looks so fresh. I have attached a few photos.

Do I have to remove the existing thin covering or just fill the holes thicker with slurry? No idea what the previous owner of the house did there. Since it looks so thin, I guess it might be leveling compound or something like that. At the edges of the holes it is loose and sounds hollow, where there are no holes it does not sound hollow. In one of the photos you can also clearly see the wet spots on the floor now that it has rained for a while.

Yes, such an old cellar is rarely as smooth as a baby’s bottom and consists of a homogeneous, crater-free concrete surface. You should remove and chip off everything that is loose. It is best to lightly tap the entire floor once with a hammer/mallet and remove everything that crumbles or flakes off. Do not destroy the floor with a sledgehammer but rather "drop" a 500g mallet loosely. If something sounds hollow, remove it! Sweep and vacuum everything dust-free. Then fill everything that is deeper than 5mm with suitable repair mortar. MEM recommends their own rubber mortar for this. I like to use Lugato R&S 1-component mortar—something you need anyway for the fillet or wall breakouts. You can also simply fill smaller unevennesses deeper with the sealing slurry during the first waterproofing coat. The important thing is that nothing is loose or crumbly anymore, and you must definitely bind the dust with water beforehand.