They mean exactly the same thing. 好吃（spoken language） 美味（written language） 好吃 is only used as an adjective; 美味 can be used as either an adj or a noun.

I don't know how to describe the two words in English. Maybe you can use delicious to instead of 好吃. 好吃 means it's really good and delicious that something tasted.But 美味 is not only means the tasting but also make somebody feel good almost immediately when they see the food. So 好吃 just point out the tasting while the 美味 means more.

好吃 < 美味 both are correct

no difference. 好吃informal,but the other is formal.