As a first step the sewer line from the inside to outside could be snaked with a video camera to see what the clog is or just snaked to clear the pipe.
Black stuff coming out of washing machine. While washing machines are designed to wash out dirt and soil build-up. You could have old pipes or roots from trees blocking the pipe. Dirt deposits after wash on bottom of drum and on clothes.
It thrives in cold and damp places. Wring out the rag in the bucket. Based on your symptom and details the drum bearing has most like worn out or the basket support busted causing the spin basket to wobble and rub into the front half of the outer tub.
Oily spots - perhaps from HE laundry detergent. Pour 1 cup of white vinegar into the rinse cup. Although it may delay or even prevent new mold growth in the washing machine it will not remove the current black stuff.
If you have black mould on your door seals it can be quite hard to remove try a good strong neat bleach but only leave on for about 5 - 10 minutes. Once it begins to agitate open the lid to make it stop. Bleach stains - sometimes from bleach sometimes from other causes such as laundry stain removers.
It is caused by having conditions where the airborne spores can survive and thrive. If your washing machine has a black jelly-like substance growing in the soap dispenser it is likely to be a fungal bacterial growth called biofilm. This should remove or take away most of the mould.
Youd have to pop the top open and remove the top tub ring and see if you have the same thing under the ring or around the inside of the outer tub. You should try to resolve this issue by following these tips. Dial half a bucket of water and add the juice or citric acid to the water mix it in the washing machine and leave for 3-4 hours.