OrangeNeuro

Congratulations and welcome to Montreal! I have lived here since 2008, I did my undergraduate and MSc at McGill. If you have any other questions about the city PM me!

In general I advise living off-campus, but if you're international the first year on campus could be a blessing. I studied in Canada for my MA and chose to live in an on-campus apartment since I didn't know the area at all, was on a limited budget, and had no credit in Canada. It turned out to be a great decision, and while some of my other international friends chose to move off-campus after their first year, I stayed for a second year in my on-campus apartment. I will also say that if you're doing graduate on-campus housing, it's a great way to meet other students outside of your field. (This is how I met a ton of Engineering students from all over the world while I'm in the Humanities!)

For Montreal, I agree with fuzzy and also second the thought that most grad students live off campus, and rent in Montreal is very affordable for a big city!
However, if you are moving from a faraway country, I think it makes sense to start living on-campus at first so that's less things you have to worry about when you get settled in. If you are able to end your on-campus lease early, then that might be worth doing once you find a good place off-campus. I know that in Quebec, the typical notice to vacate is 3 months (unless it has changed since I was last there). So, in addition to July 1 being the most common lease end date, you would usually start looking for places to live 3 months before you want to move.

Where you live is up to you. I've only ever visited Montreal but it seems like a very commutable city with a good public transport system which makes it easier to live off campus. Most schools provide a couple of benefits to living in university subsidized housing such as free internet and direct shuttles to and from the housing. On the other hand it is sometimes much easier to find cheaper housing a little further away especially if you want certain amenities such as allows pets or a private yard.

All the grad students in know in the city live off-campus. Montreal is a very affordable city. You should be able to afford an apartment off-campus, with or sometimes even without roommates (depending on location and how much you are willing to spend). The most important thing to know is that most leases start July 1, though you can also find decent apartments later in the summer. 

Check TheGradCafe to see how stressed out applicants are and see how long I can keep them guessing. Then, put pressure on them to decide in a week or less without visiting.

Usually, in Canada, similar to Europe, the PhD application process is more like a job offer where an graduate admission offer is often tied to a research position in a lab/group and that lab/group might have an agreement to sign to join that lab. Or, this could be due to the fact that your school has RA or TA unionized (most schools in Canada do) and this formal contract is just part of the paperwork. A "letter of agreement" could mean a lot of things---if you don't mind sharing some of the details of the letter (either here or via private message), maybe people can help you figure out what the letter is saying.

It depends on the school and country. I'm not sure how Australia works but in Canada, securing a supervisor is basically the only way to get admission. Unlike the US, some countries like Canada basically hire grad students at the supervisor level (i.e. the department will check all applications to ensure they meet minimum standards and then it's up to each professor to decide if that prof wants to hire the grad student or not). So if you were asking the same question in Canada, my answer would be that you are pretty much guaranteed to be admitted if the professor says they want to admit you (but you have to be careful to distinguish between a prof being interested in you and a prof actually deciding to take you on).