I think I'd be able to answer most of your answers based on my knowledge. From your post, I do not get enough information to answer to the point. I am assuming you are US citizen (not LAPR) and the girl you want to marry is Canadian citizen (not landed immigrant)
To get married, in Canada you do not need any visa you come to canada (preferably by road) go to city hall with your fiancee get yourself a marriage license. They will ask for ID's that is drivers license. Once you have the mariage license you are free to get married. SIMPLE
Still worried?? What is it that bothers you?? Travelling US-Canada? Living together?
Visiting US/Canada - US citizens or LAPR do not need visa to enter Canada, their passports are not even stamped for entry (general rule no entry in any country permits you more than six months stay unless specified, so if there is no entry stamp that means six months - you need to find out more about it, I know people who has stayed more than six months in Canada). For Canadian citizens, US authorities do not require visitors visa, passport is ofcourse necessary. Canadian landed immigrants do need visitors visa to enter US, unless their nationality is from a country exempted for visa to visit US.
To get Canadian residency, (i believe new regulations allows US citizens to get Canadian citizenship right away) you can ask Citizenship and Immigration Canada about sponcership procedure. Your canadian partner can sponsor you in Canada.
Suggestion: you can keep your US citizenship with Canadian landed immigrant status
Benefit: Most benefits are for citizens in US, in Canada benefits are open to landed immigrants special comprehensive and extended health coverage.
Again, this info is based on my knowledge of regulations and the information you provided. I am not an authority, so there are chances of deviation.