You have good questions. Lucky for you, Fizz will be the perfect fit.
Fizz mobile is prepaid service, so yes you can use it for 2 months. After you have renewed for the second month, you should remove your payment info (credit card) from your account. Your service will be suspended following the second month of service. If you don't plan on keeping the phone number, you can also use the unsubscribe option to cancel your plan.
Fizz SIM cards are environmentally friendly, they can be reused again. As far as I know, they are the only Canadian service provider to allow this.
If you know the approximate number of days between cancelling and reactivating again, we might be able to provide a clearer answer.
Read here for Fizz FAQ on cancellng mobile:
"After you cancel your plan, you will still have access to your Fizz account. All information about your plan — including your transaction history and payments — will be kept for three years."
After cancelling, the number of days Fizz will hold your number is between 60 to 120 days. Fizz support can confirm this.