Well, isn't it obviously who would win in the cooking contest without even tasting it?
Also real "villain" does not appear in a slice of life type series like this. Also, Gin already found out the true nature and identity of Zange, didn't he?
About Nagi becoming the idol, all she needs to do is just walking around in the school. Also even Gin doesn't know how it started either, so may be us viewers would suppose to be the same?