You can use bleach to clean your awning, but be sure to properly dilute the bleach and do not leave it on your awning fabric for too long, as it may reduce the lifespan of your awning. Also, it’s a good idea to test it on a small part of your awning first to ensure it doesn’t cause any discoloration issues.
You could also look at Starbright mold and mildew cleaner (they have it on Amazon) for your mold issues. And going forward, I’d suggest cleaning it once or twice per year (or as needed) with mild dish soap and make sure it’s dry when you roll it up. You can see my full process here: https://camperfaqs.com/how-to-clean-rv-awnings