"It's important to enjoy one's studies."
Translation:C'est important d'aimer ses études.
1) Yes, "c'est important de s'amuser dans ses études" is correct but it's probably not on the list of accepted translations. The main reason is that "to enjoy" is certainly different enough from "to have fun".
2) As a reflexive verb, "s'amuser" literally means "to amuse oneself". So the "s'" (oneself) is the direct object of "amuser" and you can't have "ses études" as another direct object. Literally, it would be something like: "it's important to amuse oneself one's studies".