Until you become a citizen or landed immigrant of another country Canada considers you a Canadian and they will tax any income you make. You cannot be a citizen of the world and will have to file your Canadian income tax each year.
As far as health care you are only allowed to be out of your province for part of a year (Ontario 7 Months). If you are going to be out of the country longer than that you can apply for a once in a life time 2 year extension. You will need this exemption to get supplemantary health insurance for that period.