I don't see how Kakashi could possibly find out his weakness by fighting with him like he would another ninja. Superman's weakness isn't some lapse in technique, it's a rare foriegn element that Kakashi wouldn't have a hope in hell of finding, or even knowing about.
Depends on what era Superman we're talking about, I think. If it was OMFG Golden Age Superman, he has every power ever and absolutely no weaknesses, including the ability to write his own stories. He'd retcon Kakashi into nonexistence.
Kakashi, meanwhile, has the ability to turn day into night, being a ninja and all (how else could they be so successful?). He should have no trouble making the sun into a red star.