These are all good questions, let me see if I can help you out with a few of your questions:
1. How do schools determine what "bucket" would a particular candidate fall into based on the citizenship or based on the location/country of undergraduate studies?
They will look at your entire profile to categorize you, often times there will be a question asking about countries with which you claim citizenship. Clearly if you spent most of your life in India and went to school there that will be part of how the school will view you but the fact you have international experience and are now a Canadian citizen and have spent some considerable time in the country really will diversify your profile even if you are not put outright into the canadian bucket. Remember these "buckets" exist to create a high quality student body and I'm not sure the citizenship drastically changes things for you, your experience in Canada will have a greater effect on this.
2. Will it make any difference if I send an update to my schools about the change in citizenship for R1 schools now so late in the game?
No
3. If I apply next year to schools in USA for R1, would I be considered Canadian applicant based on my citizenship or still be considered with the Indian applicant pool as I did my UG from India (and this is something that I can not change now!).
See above
This is my opinion so hopefully others will chime in as well. Good Luck!