As a PR of Canada, you are allowed to leave and come back, so long as you meet your Residency Obligation.
If you want to sponsor a romantic partner, you must live in Canada as you do so. As a PR, you cannot sponsor someone unless you are in Canada.
How long it takes depends on various things - where you're from, which office it's assigned to, who the case officer is, if there's anything wrong with your application, etc etc.
The procedure is at
https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/family-sponsorship/spouse-partner-children.html