The national parks pass is eligible for US and other citizens. However it is only good for national not provincial or local parks. It only covers park admission not camping, firewood, etc.
If you want to stay at national parks get reservations ASAP as they will be extra busy this year due to the passes.
You can get the pet info by Googling taking dog into Canada. You will need the certificate, just be sure it has each and every required element so you don't get turned back. With the right certificate, there will be no problem at all.
Land of 10,000 Lakes
2016 Forester MBS 2401R
Nights camped 2016: 32; RV to date: 35
2016 FR Forester 2401R
Towing 2014 Honda CR-V