depends on your destination within canada, and i am NOT really sure what the regulations are with regards to foreigners, but to start off,
as long as you have valid drivers license and address, (and insurance) you should be able to buy a car.
for 2k, i would think some rough and worn cars, but if you browse private sellers listings, you may find some good ones. from used car dealership, probably not.
cars in 2k range CAN BE reliable. my bro's kia rio (2003, less than $2k) had been flawless reliability wise for nearly 2 years. even in the dead cold of the winter, which can reach -40 degrees, it started and ran right on the turn of the key.
on the other hand, you will have to filter thru million + garbages to find few that will serve you well.