When you cease to be a tax resident of Canada, you will no longer be eligible to receive these benefits. You should advise the CRA accordingly to not continue the payments.
If you do receive a payment you are not entitled to, the CRA will issue a notice requesting it to be paid back to them once they identify that you were not eligible.
If you still have bank accounts in Canada or amounts being paid to you from Canada, you are required to notify any Canadian payers and your financial institutions that you are no longer a resident of Canada.
No, Canada does not allow joint filing so both you and your spouse will need to file a tax return if required.
While a tax return may not be required if your spouse has no income, it is advisable for your spouse to file a Canadian tax return in the year they depart Canada so that the CRA is informed of their change in tax residency status.