You can go to Immigration Canada website to find more information. http://www.cic.gc.ca
For most places in the US with a Canadian Consulate, if you apply for a study permit in person, it may be issued on the same day. However, I do think you need to do a criminal check for the US part, since you've been there for more than a year. The criminal check part can be lengthy and do it ahead of time. You have to go to your local police office to get fingerprinted, and send the card to the FBI criminal check bureau. It only costs around $20, but it may take up to a month to process your request.