For the roof, get yourself a pump sprayer. You didn't say how big your roof was or how large of an area needs sprayed but I'd get at least a 2-gallon. If your roof is relatively flat so you can walk on it easily, you can get/use a backpack sprayer but I don't like them on steep roofs. If I lose my balance or footing, I don't want that backpack on me while I try to regain balance.
Use 5% bleach mix to the water. That's just under 1 cup of bleach to 1 gallon of water. Spray the areas with mold, algae or black stains. Do this when no rain expected for 24 hours. About a week later, check the area again. It'll either be much better or completely clean. Areas of heavy mold or algae may require more than one dose. Repeat until everything is clean again. For my roofs, 1 or 2 doses takes care of it but if you have an inch of "stuff" growing, it may take a couple more doses.