The health care in Canada is provincial. Each province has it's own little rules. Since I saw in your other post that you are looking to move to Edmonton, you need to deal with Alberta health, best to do it directly to find out about this. You can find their contact info here: http://www.health.alberta.ca/AHCIP/contact-AHCIP.html
If you want to get more info on First nations people or some contacts, you can try to contact some bands or somebody like the Canadian Native Friendship centre at http://www.cnfc.ca/
Most of the First nation people in Edmonton are Cree or Meti's. I do believe you can get out of paying sales tax if you are a registered first nation member but don't expect that the public will look at you with a kind eye if you pull out one of those cards in a store. First nations people also get free college but I do not know if this would apply to you or your kids since you are not from a Canadian band.