the black in your soap drawer is mildew. Sadly it is quite normal, unless you are lucky enough to have soft water and hot fill, when it will be reduced. Leaving the drawer slightly open so it can dry out between uses will help, so will scrubbing the drawer and its aperture with a bathroom or kitchen spray with bleach, which is formulated to reduce soap residue and limescale, using a nylon brush. The bleach will temporarily kill the mildew. The limescale roughens the surface so soap and mildew can hang on.
You can also put the scoop of powder into the drum with the clothes, which will keep the drawer cleaner, but with cold washes may leave undissolved powder residue on them.
Your other wastes can be kept clean using Washing Soda Crystals. Spoon them into the waste and overflow once a week or so, moisten slightly with hot water (not enough to wash them away) and leave overnight, then rinse down with hot water. It is very good for dissolving soap sludge. You can also use them in your washer to improve results and remove sludge from the drum, which can smell, using the hottest wash cycle and a cup of crystals with no soap of fabsoft. If the water foams up and goes grey, that's old soap sludge dissolving.