Q. 1. What is a "Binding prayer?"
A. 1. The term "Binding prayer" does not find its origin in the Holy Catholic Church. It is a ridiculous new concept (to hook people with the latest fad) that really is a very old concept, just under a different name.
The practice of "Binding prayers" is associated with those who are involved in the Charismatic movement and who are attempting to perform exorcisms. A "Binding prayer" is an attempt to bind the devil. Any such attempt should be left to a priest (exorcist) who has the authority from his Bishop.
It is very dangerous for a layperson to attempt exorcisms.