Yes - the US and Canada share information.
Yes - the 2 year overstay in the US is going to create problems for you in obtaining a study permit for Canada since it demonstrates an abuse of visa privileges. To be approved for a study permit to Canada, you must demonstrate you have strong ties to your home country and have no plans on remaining in Canada long term. This will be very difficult for you to prove given your US overstay. If you are serious about obtaining a study permit for Canada, you will need to return to Chile (if you haven't already) and develop strong ties to your home country again before attempting the Canadian study permit application. Given your overstay in the US was so long, I would recommend that you live in Chile for a minimum of one year (ideally more) before applying. You'll want to make sure you develop ties like a full time job, property/assets, etc.
Also, be aware that as soon as you leave the US, you'll automatically be banned from that country for 10 years due to your overstay.
Good luck.
