No, the government only sets drug prices. AFAIK private pharmacies buy and sell drugs at set prices and add stocking\service fee to sustain their business operations.
In some provinces, the government is also the sole purchaser of some drugs and controls their distribution, as is the case for alcohol imports and cannabis (iirc, ex: Quebec).
This. You have to consider that Canada does not have a singular public health system since they are provincial responsibilities. The Federal government "guarantees" it, but in practice doesn't do anything other than delegating it to the provinces and equalizing funding between the provinces.
In almost all of the systems, medication is not covered unless you're a child, extremely poor, or very old.
In practice about 30% of all healthcare expenditure in Canada comes from private sources, since things like medication, dental care, vision care, and a whole myriad of other critical segments of healthcare are not covered by any government health plan.