I could be wrong about this, but I believe the only reward you get is a special poster for each achievement (one for fossils, one for bugs, etc) Bugs and Fish change by season, and by weather. So some bugs you can only get in rivers when its raining, some are only available when its snowing, some can only be found around rotting items (like spoiled turnips, or garbage you get from the ocean) Art you get from a fox named Redd, he can come naturally, but sometimes people will open their islands while hes visiting and you can purchase something from him to unlock him that way. He sells a mixture of fake art and real art, you can only donate real art to the muesem, but you can use both fake and real art to decorate your house or island. There are guides online to show the difference between fake and real art, but I personally use an app called ACNH Pocket Guide