What body in england competed with the monarchy for au- thority? what special privilege did that body hold over the monarchy?

The correct answer for the first question is the parliament.

The parliament was devised in order to limit the power of the king or the queen and to prevent them from being absolute rulers who could do anything that they wanted. The king still had a huge amount of power, but there was a check and balance system in the form of a parliament.

The special privilege that the parliament had was that they were the ones who would decide on taxes. The king or the queen didn't have the power to decide on taxes in order to prevent them from exploiting people and taking higher amounts of taxes. This was devised as a way to protect the people and make them only pay what was necessary.