In this context fairly is used to mean "a bit" whereas rather is meant to mean "a lot." It's just a matter of degrees, really. In other contexts the two cannot be used as interchangeably as Rather also means "preferable" and fairly means "justly" or "impartially" (See the examples.) Fairly vs. rather: “I’m fairly tired” means I’m tired but I’ll get through the day, while “I’m rather tired” implies I’m probably going to go back to bed. "I thought the evening went fairly well." means that there weren't any problems & the speaker has no complaints. "I thought the evening went rather well." means that the evening was fun. Other definitions/uses of "Rather" and when not to use fairly: "I would rather get delivery then cook." or "I would rather go dancing then see a movie." In this case you can see that by substituting 'fairly' (I would fairly get delivery then cook) doesn't make any sense since in this context rather is meant to imply a preference between two choices/suggest an alternative. Other definitions/uses of "Fairly" and when not to use rather: "He felt that he had not been treated fairly by the police." "They were only asking to be paid fairly for their time."

In this context, you say "rather astonished." You can't really be "fairly" astonished because astonished itself means "very surprised." It doesn't really make sense to say "mostly very surprised." In this sentence, "rather" gives emphasis to the adjective, "astonished."