Discoloration of roof

Thanks. This really is not a typical residential metal roof installation. This appears to be some sort of (probably) aluminum panel used over a walkway or a patio or something? This is just a "single skin" sort of application, correct? First of all, I question a bit whether this panel really should have been used this way. There is a chance water is getting through the panel seams. Overall, though, this looks like you're getting condensation on the bottom of the panels and the condensation has created mildew. Ending this problem would likely require entirely different construction with insulation and perhaps ventilation. You could try cleaning the underside of the panels well and spraying closed cell urethane foam to them. Not sure that would work nor how attractive the end result would be ... but it might help.

Can someone explain to me the numerous dark spots on the underside of this roof? Also, why is there rust on the top, and what can I do to solve this?