You absolutely have to use Canada's definition. Some countries don't even have common-law status and Canada's definition is what you use when you apply to immigrate to Canada.
If your jurisdiction said common-law only exists after, say, 32 years of living together whilst singing a specific song and doing a specific dance on the anniversary of cohabitation, and you forgot the words on the 27th anniversary, Canada's definition would still apply.
They won't get confused thinking it's a marriage because the part you're talking about literally asks about common-law relationships, right?
For the final question - you put in what you know, and you attach a letter of explanation saying you don't remember the precise date of birth.