you can enter Canada as an american - but after 6 months, you will be required to EXTEND your visitor status in order to be allowed to stay. while you are VISITING, you CANNOT work or study, your fiance will be required to support you - unless you have enough money to support yourself.
IF you need health care you will be treated for anything urgent, and then you may be BE BILLED (depending on which province you are living in). You will not be eligible for the free health care until after you become a
PR. After you are married then you can apply for permanent residency.
You cannot apply for citizenship until at least 2 years, maybe 3 after you become a permanent resident.