1. They are synonyms, almost the same. All mean beautiful, can be used to describe human being, or stuffs, or scenery. For example:
她很美。她很漂亮。她很好看。She is very beautiful.
这条裙子很美。这条裙子很漂亮。这条裙子很好看。This dress is very beautiful.
这里的风景很美。这里的风景很漂亮。这里的风景很好看。The scenery is very beautiful here.
2. Only 好看 can be used to describe those stuffs that have good contents so as to make you pleasurable, such as good books, good movies, etc. Instead 美, 漂亮 especially refers to the outer look more often.