1. No, you cannot. You have to inform IRCC when your country of residence changes. So when you move to India, you will have to update your profile.
3. All applications are electronic. IRCC will change your VO to NDVO and NDVO will issue your the PR visa and COPR and you will be asked to send your passport to NDVO instead of CPC Ottawa.
It is not the VO that is slow and other are fast. All applications are distributed based on workload. However, each office has different priorities, and some applications will take longer then others. Processing applications is a legal process and not a one size fits all formula. Your application is as unique as you are. So all those who are relying on Data and trends will be disappointed. If the data and trends were that accurate, then IRCC would be using them to increase productivity, but unfortunately, that is not how law works. Just as two murder trials are not the same, two cases before the supreme court are not the same even if they may have similar facts and the same same lawyers.
Thank you for your elaborate answer! It makes more sense to me now.