That downspout should not be terminating water on that roof. It needs to be extended over and run down along the house, and then have an extension to run the water away from the house. What you have now, is a rotted roof waiting to happen, if it hasnt already, besides the unsightly look on the roofing itself.

Good advice above. Some folks don't like that visual so it should, at a minimum, have a B-elbow directing the water in the appropriate flow pattern.

As far as the algae, get some "Wet and Forget" and do a couple of treatments. Should clean it up.