1. Check the instructions.
2. While possible, I'd recommend against it - some places (customs regs that is) and carriers are picky about sending passports, and then if it doesn't arrive, you have an issue returning to Canada (as a citizen, you'll need the Canadian passport to board a plane back).
3. I'd say it is far better to apply from within Canada - go to a passport office location and ask for it to be expedited (they may want to see a ticket) and choose the option to pick up. This might mean getting up early and queuing.
If you want to apply from abroad, it's possible - you just need to give enough time (I think they say 4-6 weeks? check online). But the biggest constraint is that if you have some issue with any of your docs while abroad, it'll be a pain to get them. In Canada you'll be able to go back the next day in most cases.