Answer to your questions
1. Yes they will update AOR status only if the application is complete. They will not update AOR is incomplete. Incomplete application will be sent back. eg. missing signature, requested documents not attached e.g language requirement , photos not sent, etc.
2. It could happen very next day, from AOR to inprocess. Your status will show in process once it is received and they enter it in their system / acknowledge in their system by the receiving IRCC location to actually start the adjudication of the application.
3. They will send the application to the nearest IRCC centre that will be their preference. Like for eg. if you live it Toronto, your application will be preferred to be sent to Toronto location, if they are above their threshhold and the work load is less on the next office near to toronto, it could be sent to any neighbourhood location could be Scarborough, Mississauga, Hamilton, If the entire Ontario province office are over loaded only then it will be sent to neighbouring province, thats how it can be sent to any IRCC center in entire Canada.