I can promise you that on my forms there was a section were we had to confirm the exact date we entered in a common-law relationship. I would double-check, if I was you.
Regarding the trip abroad, in my opinion, I would say that a month could still count as a long vacation;
if that person's official address/residence remains the same as their partner's, it doesn't cancel out the common-law relationship. But
I would 100% be upfront about it with IRCC, even if it meant sending a webform to explain it further.