Your infestation is likely mealybugs, especially if they have a cottony, fuzzy appearance and feel sticky. The black residue that you see is the result of the honey dew that the insect secretes. A mold then grows on top of the honeydew and that is called Black Sooty Mold. The sooty mold won’t harm the plant unless it is excessive and prohibits the plant from photosynthesizing. It looks as though there could be a fungal leaf spot issue also. For an mealybug infestation of this magnitude, you should prune out and dispose of the affected plant parts. If it is excessive, you probably should consider replacing the plant. To keep the situation under control, you might want to consider one of the Bayer products. A systemic insecticide plus fungicide would be your best bet.