Hope I can help you out since I have been longer on this immigration thing than you

Firstly, you can easily apply for her sponsorship after the marriage. In fact, since you have been in a relationship for 2 years you can apply as common law right away, but cases such as those are harder to prove when you can be way better off if you both are married and then submit your application.
Secondly, since she is from a visa exempt country she can live with you after marriage and you can apply for sponsorship inland. However, the inland process is longer and you have no right of appeal, while the outland process takes lesser time (depending on her country's visa office). The onus is on you guys to decide if it should be inland or outland depending on your situation.
Yes, you can marry her in Canada and she may or may not have to travel to her country depending on your decision to apply inland or outland.
For the spousal sponsorship applications you need to prove that your relationship is genuine by producing evidences of trips taken together, email log, phone bills, gifts exchanged, the works, you get the picture. I would suggest that you keep a record of all the above mentioned evidences from now so that it is easier for you guys to prove that your relationship is genuine and that you have a speedy visa processing.
You might want to check the Citizenship and Immigration website
http://www.cic.gc.ca/english/information/applications/fc.asp which includes all the information you might need to sponsor a spouse. If you have any other questions, this is a wonderful forum and Im sure everyone would be more than willing to help.
You might also want to read this thread from a senior member on this forum. It is very useful...
http://www.canadavisa.com/canada-immigration-discussion-board/spousal-sponsorship-t46995.0.htmlCheers
