Every shelter has different standards for length of time you can stay, best to check with those in your area. I've never heard of any that have a cost for clients associated, that could be more of a hostel situation?

Often you'll need to get connected with local social services to get access, they may be able to expedite the process or help with more connected services.

If you are asking in general then have a look at the Homeless Hub site, they have an incredible database. (https://homelesshub.ca/)