Nobody knows the exact answer to your first question. I believe I've seen numbers around 200,000, but that was a guess, and it was years ago. Presumably it went up since 2016 due to people fleeing the US.
People work illegally by getting paid "under the table." This means they are not on the employer's books. It's more common in construction and the restaurant industry than elsewhere, to the best of my knowledge.
I have no idea about how they rent - I would assume they would stay in boarding houses, and those types of places, or maybe even places owned by their employers in the case of construction, agriculture and mining projects outside of cities. It's very hard to rent in a city like Toronto without some kind of status.
Canada has a way less severe problem than the US for the simple reason that we share only one border and it is with the US. Until very recently, very few people snuck across the border into Canada. Most people here illegally over-stayed their legal status. That has changed recently, but modern technology makes it very hard to cross the US-Canada border illegally, at least in the east.
