Your total budget will be tight if you want to live alone, you best bet is to share the rent with roommates as most reasonable 1 bedroom apartments in locations that don’t require a car will be 1100-1400$. If you are looking for roommates online, I suggest you also use the word “colocataire” which is the French word for roommate (word for word would be co-renter). Just know that downtown/university areas will be more expensive for everything, especially if you buy take out food, then be ready to spend 20$ for a sandwich.
For transportation, the bus and metro system works in Zones. Zone A is montreal and is going to be ~60$ as a student with taxes per month for unlimited use (maybe student discount doesn’t apply if you are foreign, so in that case it will be ~100$). For the other zones (for going outside of MTL it will be more expensive, check the prices here: https://www.stm.info/sites/default/files/pdf/en/a-tarifs2024.pdf). You could also try to ask the place you are getting your internship to pay your transport pass especially if they require you to be on site!
Also if you are not from Canada and you want a local phone number, avoid the big/premium companies (Rogers, Bell, Telus and Videotron) at all costs. Instead use Fizz.ca and PublicMobile.ca. Fizz has the potential to be cheaper if you disable unlimited SMS (you just need to add balance to your account and it becomes pay per use) and with data rollover (unused data is transferred to the next month) but if you are a big data user, public might be the better option with unlimited plans and the like
For gym I have no idea of the prices, maybe that means I should start training though…
Also please save some money to try some real Québec poutine !!
I forgot to say! If you don’t have them already, place some leftover money to get a used winter coat and some boots (maybe the boots won’t be needed, sometimes snow is late). September it will be fine, but as november comes closer it will start getting cold