The "white stuff" is powdery mildew. Neem oil spray will work to control it, do not spray in hot sun. If you are conventional gardener you can use a spray containing chlorothalonil to control mildew and other fungal diseases.
The black edges could be from the mildew or could be from something else like windburn or spider mites or another fungal disease.
Note: never use a spray containing sulfur on cucurbits. It works well for fungus, just not on cucurbits because they are sensitive to it.