Interesting topic. Have you already contact the official organizations? In my opinion you can always apply, but of course you to know what chance of and open work permit will be.
You can contact some local real estate agents, share your question on the social media and ask around in Montreal. This will probably give you more helpful leads then on an immigration forum about Canada.
With the PMP you will probably be more interesting for companies. A couple of years ago I did the same with the projectmanagement certificate for Prince2. But of course it's not a guarantee at all.
I would advise to post your job on sites where you can post your job for free and then specify for your ad for the type of people you want to hire. This will probably give you a bigger response.
Never used it in Canada, but I've used it in other countries. Great experience, check the reviews. You can also look at booking or other similar websites. It's worth a try and saved me some money.
Depends on the landlord / organization. Make sure you have a proof of income, identity papers and if you're a student maybe a statement from someone (like your parents) that pays the rent if you cannot pay it.
Looking forward for some interesting answers on this topic. If possible with the right information from official (VISA) organizations in the UK, London.
Hard to say, depends on so many factors. Looks like you have a good education and work experience, of course that will help.
Have you already started searching for a job that meets your criteria?