Yes, as long as you have a valid visa or eTA. It is imperative that you have it as this is your travel document. In addition, you must travel with your valid work or study permit because you will be asked for it when you re-enter Canada. Your permit is your legal status in the country, while the visa or eTA is your travel document. 

If Immigration Canada discovers that you have not complied with the conditions of your study permit, you may be asked to leave Canada and/or this element may create a negative immigration history that could have repercussions to your future processes. Please review your permit conditions and restrictions very carefully to avoid misunderstandings and contraventions.

It is possible that your passport expired before the end of your study program or job offer. Canada cannot issue a permit beyond the validity of your passport.

For the moment only to Montreal, Toronto, Vancouver and Calgary.

No, a work permit or study permit is not a visa. You will not automatically be issued a visitor visa if you extend your work or study permit. If you need a new visitor visa, you will need to file a separate application. The visa is required if you want to travel and be able to return to Canada to continue your studies or work. Do not leave Canada with an expired visa (even if your study or work permit has already been extended), because you will not be able to return without a valid visa.