If you are Canadian citizen -you can stay outside Canada for a long time
That's right.
and you are not required to come back to Canada while having a PR, you need not go back so as not to
lose your PR status, right?.
That's right which would affect her if she loses her PR and then changes her mind about living in Canada, maybe she becomes disabled and nobody is there to take care of her in old country
Further question is: do you have any responsibilities that you need to do as a Canadian citizen
even if you are outside Canada like filing your CRA tax?
No, if you are not living in Canada and have no assets in Canada, you can have yourself listed as a non-resident for tax purposes. I am not sure how it works though if she is getting a pension from Canada though
Is there anything that will forfeit your Canadian Citizenship?
Only if they find out that you have lied to get your citizenship or to get your PR or possibly treason