Of course you can leave Canada and take care of your family. She's applying by her own means, your invitation letter does not really matter. She can try to submit a webform and ask about her application.
Quoted insurance instead of a real one: https://www.canada.ca/en/immigration-refugees-citizenship/services/visit-canada/parent-grandparent-super-visa/eligibility.html
Officers have the discretion to determine the length of an extension. If an application meets the necessary requirements, officers should consider the following when determining the length of the extension:
the applicant’s means of support while in Canada
whether the applicant has provided...
We recommend that you submit a new online application if you submitted your visitor visa application before September 7, 2021
https://www.canada.ca/en/immigration-refugees-citizenship/services/coronavirus-covid19/visitors/visa.html
Covid, Afghanistan and Ukraine make the whole processing time thing worthless. As @canuck78 said, if you can't wait for at least 6 months to get a decision, just don't apply at all. Processing time will disappoint you.
Yep, your brother will have to present his own application, showing his own proof of funds and ties to home country. An invitation letter from you won't hurt.
Check the eligibility for super visa: https://www.canada.ca/en/immigration-refugees-citizenship/services/visit-canada/parent-grandparent-super-visa/eligibility.html . You can apply for your mom. How old is your brother? I'm afraid he'll have to apply by himself by showing proof of funds and ties...
You don’t have to do anything, the IRCC does not really care about travel plans. In fact they advise not to buy airline tickets, hotel reservations etc.
Here you have it, 154 days, last update oct 25.
https://www.canada.ca/en/immigration-refugees-citizenship/services/application/check-processing-times.html It's just a losely estimate, so don't base on it.