Question

How worried was Cortes about his actual authority to act in Mexico?

Answer 1

Cortes was not worried at all about his actual authority to act in Mexico, since he was given practically free reign by the Spanish Crown to do whatever was necessary in order to bring back as many riches as possible. 

Answer 2

Cortes was not worried at all about his authority to act in Mexico. He was given free reign in Mexico by the Spain crown, and he used its authority to justify all sort of measures in order to acquire and maintain control over the territories that were recent discovered. Cortes is still remember as one of the worst spanish conquistadores, because of its reputation and acts with the local people.