Thanks FF.
I'd be interested to see what the others come up with for the slabs, but I would say...
Weeding
Powerwash
Brush kiln-dried sand into the joints on a nice warm sunny day. (So that the sand doesn't take up moisture and clog up.)
The wall...
A retaining wall I guess. That would account for the damp penetration. Ordinary blockwork with one coat of render (you can see the mortar joints clearly because they are more porous than the blocks.)
A second coat of render would hide the joints, but I wouldn't advise it now. You'll have to do quite a lot of preparation to get it to bind.
Consider "scatting" the wall. Otherwise known as "roughcast" (NOT pebble dash.)
Simple sand and cement mix, but sloppy. Hurl it on with something like a small coal shovel, or rent a proper scat-gun from a Hire Centre. (They'll probably call it something else - it's a receptacle with a handle on the side, which you turn to flick the scat out.)
With two or more coats, you could leave it at that. Pick a colour of sand that you like. Even use white cement.
The downside is that there is no coping along the top of the wall. Overhanging tiles/slates would look good, and help shed the rain off the face of the wall.
Painting is an obvious choice, BUT, without a coping, rain will run down the face and stain badly. Very soon, it would start to look awful.