It is always better to apply from home country, because if you are not the permanent resident in the other country then there are strong chances of getting visa refusal on the basis of home ties and level of the establishment................
For additional medical tests the initial tests should be received by the CHC, they will check them and then ask for further medicals if needed, but as you are saying they haven't received them in the first place..................
After medical if every thing ok then visa will be issued in a month but some times if u applied a lot earlier visa is issued two to three weeks before the classes...
Quebec Acceptance certificate is a document you need before applying for visa if your college / University resides in Quebec, follow the link...........
http://www.immigration-quebec.gouv.qc.ca/en/electronic-services/caq-electronic/index.html
You have to schedule a pickup using some courier. University will not ask more money they will ask to arrange the pickup using some friend or courier.TNT charge almost 4000 for pickup. Email ur course adviser she/he will email u the whole procedure.