You cannot do a basic level with a machine on wet soil. That will compact it more. You need to loosen the compaction first. This is true compaction done by a machine on wet soil. The weight of the machine squeezes air out of the soil which is replaced by water which then evaporates. Your soil will be hard as concrete when it dries. You should not need more topsoil unless you have low spots in the yard that don't drain well. Bobcats do not do a great job of surfacing the soil with a traditional box blade, but your yard is rather tight with trees and shrubs. I would be tempted to use something like a Harley rake as pictured here. You undoubtedly have a different name for the tool in NZ. These machines work only at the surface of the soil and can be adjusted with much more precision than, say, a hand held rototiller. There is also a rototiller attachment that fits a Bobcat that would go a little deeper into the compacted area. These are much better controlled when on the Bobcat. The problem with hand held rototillers is they buck up and dig down depending on the soil softness, rocks, roots, and pipes. This up and down action leaves an uneven subsurface and an unequal depth of fluffy soil on top. When that settles it settles down to match the uneven profile of the subsurface. But when you use a machine mounted rototiller, you don't get that. The result is much better. This should help you talk to the Bobcat man. Then you can level it by hand after the surface is loosened. There should be good drainage out away from the house. Bringing in more topsoil usually interferes with drainage, so don't plan for that.

You fix it by removing everything down to the studs. After you have removed -- rather than tried to repair -- that messed up drywall, you install new drywall, and tape, mud, and finish it. If it is going to have exposed corners, you should install corner bead before taping, which will protect from damage.

I can't give you answers to all of your questions, but I can answer a couple. 1. That vertical crack looks like a crack in the foundation caused by settling. It happens in a lot of older homes and I don't think it is super serious, but it could settle more over time, so you might have to re-do a repair at some future point due to additional movement. 2. That looks like normal cracking in old plaster...not an indication of anything worse. 3. The black stain is not mold. It is stain damage caused by water sitting on top of the oak parquet, either from watering plants sloppily and not cleaning up, or from a leak coming through the wall from outside. There are various ways to try to clean this up (just Google), but in my experience it's not possible to make them disappear completely as it's not just on the surface, but has penetrated down into the wood a bit. I once had to deal with this and finally used a power sander to physically remove the stains, and then refinished the surface to match the surrounding area as much as possible. I probably had to remove 1/16" of oak to get to undamaged wood. 4. How did you get debris behind a baseboard in the first place? In any case, the easiest thing would be to pry it off, clean behind it, and reinstall....and maybe cauld the top edge with latex, paintable caulk. 5. If I were repairing that wall, which looks like concrete with patches of spackle or a plaster skim coat. I would sand only enough to remove anything that is loose, and then use a 12" wide joint knife to flatten the surface with joint compound.

So, to be clear, I wasn't really talking about the drywall - I was talking about the backer-board behind the tile. That should be 1/2" cement board or something similar. You won't be able to feel it, you will need a visual. If it's a bad install, two things that can happen: 1. There was no waterproofing and so the water seeps through the grout and such and into the backer board. 2. The backer board sits too far down on the tub, without an air-gap. And because of that it is wicking up water from the edge of the backerboard. You will only be able to determine that (without taking the tile off) by getting a visual of the back side of the backer board. If the bottom edge of the backerboard looks dark from moisture, it will have to be redone. ____________________ Since you say that the door is properly caulked, the other place I'd look is the junction between the tile and the tub. That appears to be grouted when it should have been caulked. Anywhere there is a change in plane it should be caulked, not grouted. To do a better job, fill the tub with water first so that there's weight in the tub before you caulk. Yes, water sitting on that tub/tile edge over time can cause moisture to wick horizontally through the grout and cause the issue you see on the drywall. Caulk the tub/tile joint to prevent water that sits there from being drawn into the grout.