The floor. No reason to tear up the existing concrete. The dirt may need to be dug up - it depends what's underneath it and how stable/compacted it is. If it's more clay than dirt, then It probably won't settle any further. It may pay off to have a concrete contractor do the work.
The wall; I don't know. It depends how thick the wall is (was.) Sounds like it's been compromised quite a bit. The concrete could be patched, but It wouldn't add any strength - only 'beauty'. If you hire someone to do the floor, they could probably put a steel girder (or 2) in front of the wall to stabilize it. I had someone do that in my basement because the walls were bowed. He only charged me $100 to put in 5 girders. (I got a great deal.)
..Anyway, a job like this you can do yourself, but you're not likely to save much money & it will be very time consuming. Shop it around.