1- Should I include the photo pages from both passports in the application?
2- When I receive the PPR, can I present both passports? I checked some related posts here and they are all saying just one passport should be presented.
3- When I got the PR card, can I use any of the two passports together with the PR card to enter Canada?
The most straight-forward solution is to renew the expiring one but it's not that easy in my case. I'm sorry if the above sounds weird. Thank you so much in advance!
1 - Yes. I believe you will put one as your 'main' citizenship. It's basically up to you which one. There are not many implications to this really. However I would suggest that you make sure that the one that is directly linked is one for which you have a valid passport at all times (until you acquire Canadian citizenship).
2 - No, just one. I believe it should/must be the one you put first. I don't know if IRCC actually cares about this, just administratively they're not really tracking two different ones. (I believe the other is there mainly for background check purposes)
3 - Basically, yes. Note however: getting on an airplane and being admitted to Canada at a port of entry are two different things.
At a port of entry (airport or land border): if they can identify you as a PR (either valid PR card or an expired one AND some (any) identification that lets them link "you" (the PR) and "you" the traveller), they 'shall' admit you. Usually the PR / individual number (called UCI), some photo identification and first/last name/DOB matching between these will be enough. (That is, border officers look it up on their computer, and in principle, doesn't matter which passport or technically even if you don't have a valid passport). [That said it is ALWAYS preferable to travel with a valid PR card and - if possible - a valid passport and ideally the same country passport that's linked. If there's a problem at the port of entry, it is you who will have the issues.]
Getting on an airplane is the rub: first, you need a valid passport to get on a plane almost anywhere these days. And to get on a plane to Canada, you will need the valid PR card (small exception is US citizens). And while technically there is no requirement for the PR card-noted nationality (only one - on the front and back) and the passport to match, the airlines have the final say (because they are paranoid about getting fined). [Note, it mostly doesn't matter which nationality is used to book your airplane ticket - the main thing for airlines is that they can see that the person carrying the PR card will be allowed to enter Canada. Dual citizens are not rare these days, so they're used to that issue.]
So again: will be much easier if the passport you use to get PR status - and is noted on the PR card - is the one you can always have valid.