It's possible to do it but the ETA requirement may complicate thing a bit. If you are an american there will be no problem, you won't need an eta to fly back to Canada.
If you're not an american then it can get complicate. To board a plane to Canada from a visa-exempt country you will need your passport with one of those document; your PR card, a travel document (issue by canadian ambassy in your country) If you don't have those, you will need an ETA and as a PR you are not allow to get it.
Yes, you can land and return to your country to wrap up your affairs. You must give a Canadian address for the PR card when you land. You can give a friend or family member's address but the CBSA officer may refuse to allow that. If they do, you will need to apply for a PRTD when you are returning to Canada.
Is not a problem. Only potential issue comes from eTA (which cannot be issued to a PR). If you don't have your PR card (whether that be by staying until it arrived then leaving, or having it sent to a friend and couriered to you), you'll need a PR Travel Document to board a plane, or to fly into the USA and rent a car to cross the border.