Hagop - i can tell you be very careful, especially with the marketing of flight schools anywhere in the world.
You have to separate the "business" side of flight training from the "career" part. What i mean is that every flight school around the world can give you licensing within a year (if you do it full time), you will pay a ton more though, honestly they just want your business. I once considered going to the EU to do my training then made the decision not to because of the very issue you pointed out. Citizenship.
There are many jobs in Canada with regards to regional, its a very saturated and small market, no comparison to the US which many ppl mistake. It is one of those markets where, you have to wait your turn in line, you will end up somewhere might take a couple years though.
HOWEVER, it would be very risky for you to come to Canada, do your licensing, and hope to god that an airline will sponsor you after your training, or until you get 1500. Even with 1500 you cant get into Westjet/Air Canada/Porter because as i said it is very saturated. I'm not saying an immigrant cant get a job as a pilot in Canada, but HR departments may differ.
The ABSOLUTE minimum you need is at least a passport (not going to specify which one) that can allow you to freely fly interchangeably between Canada and the US. IF you did come here, you'd be putting a lot of trust into one flight school, and trust me even if you were to become a FI with the same school what happens if everything doesn't go to plan? whose going to hire you under visa? not many people....its a big risk, think about your time and money. The government is pretty ok with extending visas but you have to prove you have a reason to, flight training is only temporary the job after might be too!