Certainly it can be used as a mediator, even when treated as a state rather than a trait. Suppose you're studying the relationship between results on an exam and desire to interact with other peoples. The relationship would be undoubtedly be partially mediated by negative core self-evaluation.
When studying states, it's important to keep in mind that all the data must come from within the period of time that the state exists.
I think it can not, because the initial view is already formed with a negative charge. So that objectivity to the problem does not exist, even tend to have an assessment before doing the assessment that should be. Thankyou