Is it possible to pay and test Monitor Backlinks only for one month and then cancel if I want to?

You can subscribe to one of the monthly plans, as they are renewed month to month. You can upgrade, downgrade or cancel your subscription in the next billing cycle (for the coming month in your case). 

To update or cancel your subscription: 

go to your Account page: https://monitorbacklinks.com/app/account
click "Plan and Billing"
then, click on "Update/Cancel Subscription":

Updated on: 24/08/2019