"an illegitimate or unjust exercise of one's circumstantially conferred ability to do as one is called"

- License.

Explanation:

'License' is usually described as the 'freedom or liberty deviate from the established norms and act with irresponsibility'.

As per the question, 'license' would be described as the circumstantially allocated ability or freedom to deliberately deviate from the rules and use one's conferred capability to practice illegitimate or inequitable activities as one finds it pleasing to do. To illustrate;

'Liberty to express your views should not be taken as a license(freedom to deliberately deviate from rules) to disseminate terror in the state.'

adverb is the answer i believe.

the students want to see the great sphinx of giza, which is very popular with tourists.