I have begun mining AUR with my Baikal miners...the coin has an interesting story behind it, but so does Iceland.
I am an Australian, as are my family . How hard would it be for my family to move there? What are the residency laws? How do you get citizenship? Are outsiders welcome?

Best way to move to Iceland is by getting a job in Iceland where the employer files for a jobs visa based on your skills.
Second best is by finding a spouse from Iceland and marry him/her.
You can also check this out here:
https://utl.is/index.php/en/icelandic-citizenship