Carl, the black stains are mould. May not be the bad stuff 'stachybrotys' but I woudn't take any chances... mist the mould with water, then use bleach and water to wipe the area down, and cut away those studs/plate gently and bag them and get them out. Wear an N95 mask (not a painters mask, althought they look similar), gloves etc., turn your hvac off and ideally have a fan aiming outside to negatively pressure your work area (may be overkill, but it doesnt cost any $ to remove it this way, and its for your health) For your basement wall, you could fix it a few different ways, one is just plain old damproofing tar, but i like the idea of cleaning, priming and using a self adhering membrane (like blueskin). This product will stretch to cover any potential cracks... but also should be mechanically protected (i.e. covered with board). also make sure you dont just backfill with mud, use a clean rock (like a pea gravel) from the weeping tile up along the side of the basement wall, then use 8-10" of clay and a few inches of topsoil for sod. The clay will help shed water away from the house, and the pea gravel will mimimise hydrostatic pressure from water the in ground against your basement wall (which is why it leaks). A bonus would be blueskin then a plastic membrane (kinda looks like lego) that creates a small airspace between the mud/rock and the foundation so that any water that gets there will drain down to the tile... after all that make sure you have a good slope away from the foundation and rain water leaders down and at least 4' out during rain...

ak