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1. In my opinion it is unlikely, partly because dry skin is a common issue in Canada due to its dry climate in many areas. The condition is quite common, as evidenced by tons of Vaseline and Aveeno products on store shelves across the country.
2. That is perhaps your only viable chance to continue in your PR status. However, to enter Canada, you will need to have a conversation with CBSA officers, and it is unclear what you are planning to say regarding your status.
3. Until you are stripped of your PR you remain PR regardless of your compliance with the residence obligation. So provided you are let into the country without PR-related consequences yes you can work etc. You will need your SIN for employment, PR card is irrelevant for that.
4. Health insurance is a provincial matter. Generally you should have access to it according to provincial rules, e. g. in most provinces you would have access to it after a 3-month wait period after moving into the province, while in some (e. g. Alberta) you would have access to it immediately after resettling from abroad. Note though that if you are just "silently" coming back through U. S. border then you are "imitating" the situation that you never have left, so in principle your health coverage in that scenario would be uninterrupted as you would be just a resident that for some reasons did not use health coverage for a long while.
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