Hello Honestgirl,
Firstly, Congrats for getting the PR.
Well, it depends on what status you are living in Canada, eg - work permit or biz visa etc.
When they say U have been granted PR, You have to submit your passport for stamping. This is just a process which is imperative to follow and I am sure their is a time limit to do so. After completion of few yrs u will be awarded with the citizenship of Canada. It legally gives you the status to stay Permanently and you no longer have to apply for extension to stay in Canada.
No need to fly in and out of the country, thr is no logic behind tht. You will be required to fly in and out of the country only if your visa is expired or you are applying for visa under another category.
In your case no need to fly out of the country. once they stamp you the visa its done and then they will explain you when to apply for citizenship or Canadian passport claim if you want to, no compulsion. If dual citizenship is legal in Cad.
I would recommend you to call the immigration officer, whosoever is take care of your file, talk to him/her about your issue or query and they will be glad to show you the way forward, immigration dept of all country change their procedure regularly with some objective so better spk to them.
Hope this it help. All the best...

Thanks
Rochelle