It won't take much longer to get your AOR, but some people on this forum are saying that they haven't received AORs yet although their applications were received by CIC earlier than yours. So, you just need to be a bit more patient on that end while IRCC does its job.
1) As for medical, I do not think IRCC cares which country carried out medical as long as the medical was done by IRCC approved doctors. That said, it's better to be sure than sorry. I'd call IRCC if I were you to be sure and ask the agent to send you a follow up email. Email is just for your record in case call centre agent gave you the wrong information.
2) As far as processing goes, AOR (acknowledgement)->SA (sponsorship approval). Then, IRCC process your parents which is why they ask for PCC, medical. Once that is passed, you are at the DM (decision made) stage where they l ask for passport for PR stamp. That's how I understand it.
3) Again, I'd ask IRCC for clarification when that happens. They used to send PR applicants to Buffalo, NY so they can officially "land" in Canada from a foreign state. But, it was cancelled due to the obvious ridiculousness of it. That being said, you will most likely NOT get DM (decision made) within 8 months. So, it's not worth it to worry about something that has not happened yet.
For now, wait for AOR patiently and play it by ears.
I hope that helps!
