Thank you for sharing your situation and question with us.
It is great that you are looking into this type of information.
Regarding your first question,
Generally, to find out if someone has fulfilled their residency requirements, each time a Permanent Resident re-enters Canada, the Officer will count back 5 years from the date the permanent resident has re-entered Canada.
In that 5 year period, if the permanent resident has not accumulated 2 years (730 days) of physical presence in Canada, then it may be determined that the permanent resident has lost their PR status.
You can find information on the process that is followed when entering Canada in this Citizenship and Immigration Canada (CIC) ENF 23 - Loss of Permanent Resident Status manual.
Here is an excerpt from the manual on what happens at the port of entry,
and
The onus is on each individual permanent resident to meet their own residency requirements. This means that it is up to you to ensure that you are meeting the residency requirement within each 5 year period and that you are also keeping track of your time spent inside and outside Canada.
It is your responsibility to ensure that you are fulfilling your residency obligation.
In terms of proofs either to prove that you were in Canada or that you were outside of Canada you may want to keep:
*Airplane tickets/boarding passes
*Bus tickets/boarding passes
*Accomodation/Apartment information such as Lease, Rent Receipts for the time that you are in Canada
*Hotel receipts
And any other documents that can prove the time you were present in Canada in the event that you were questioned by an immigration officer and asked to provide proof of your time in/outside of Canada.
You may need to hold any mail or have any mail you are receiving redirected to another address where someone can receive your mail and inform you of what is being received.
You may also need to look into some type of health insurance as their are certain eligibility requirements in relation to provincial health coverage when leaving a province.
-You must live with the child, and the child must be under 18 years of age.
-You must be primarily responsible for the care and upbringing of the child.
-You must be a resident of Canada for tax purposes.
With online banking, it may be possible to manage your accounts and payments while outside Canada. It would be important to keep up with your payments and keep an eye on your account activity.
It may be best to contact your financial institutions as well for some further information regarding this type of situation.
I hope this information is helpful. Please let us know if you have further questions and if there is any follow up to your question/situation.