A tourist visiting Canada and staying in a hotel is generally not eligible for their nationalized health system. They expect payment/etc just like most other countries would. I don't know the details, but I wouldn't be surprised if they offer free healthcare to citizens of comparable countries that reciprocate for emergency conditions/etc, which would be fairly logical.
I doubt it. I think you're expected to carry travel insurance. I know as a Canadian I don't get covered out of the country by provincial health care.
And people here routinely get screwed by discount travel insurers that refuse to pay up when they get sick in the US. My extended medical insurance, provided by my employer, includes decent travel medical, though.