Once obtained could I leave the country for let's say 5 years and come back after?
Yes.
And could that Permanent Residency coexist with Perm Residency in Canada?
There's nothing in NZ law against that. You would have to find out what Canada says.
Finally, do I need to be in NZ when applying for/obtaining Permanent Residency?
No. But it's not a straightforward no. You would have to have met the conditions previously, and you would have to be applying within a very brief time of having done so. See this page
https://www.immigration.govt.nz/new-...-resident-visa, and the Check Criteria button will take you on to the details.