When booking your C class ticket, AJX will first of all try and use ANA. After that they will use a Star Alliance carrier and after that it'll be whoever flies to where you live. Some of the Australian commuters use Singapore Airlines (Star Alliance) but many use Qantas (OneWorld) and the Company does not seem to care too much, probably because SQ is so expensive even if it is Star Alliance. So, yes, if ANA doesn't fly to Calgary then Air Canada would be an acceptable means of getting you home.
If you move you just change the form telling them where you live and you'll get a ticket there instead. There's no problem with changing during the contract. If you have a 'home' in two places (and can show them evidence of such) then you can choose each month which one you want to fly to. Only one, though, not both :-)