I'm kind of stuck on the "Find a way to get home with the recently discovered information" part. Does it mean that the way to get back from the island isalready implemented? Or that some clues are available? Maybe I should just keep on mining for something to happen?
Sorry, there is no quest that says this: "Find a way to get home with the recently discovered information"
If you mean the quest that says you need to start thinking of another way home, then try talking to Kora and Quila
When starting the Island Arc, the game tells you to save and that the end of the Act isn't yet implemented.
No, doing something over and over again will never be required in the game.