Administrative hearings are much less formal than court hearings, but you can still object to certain things that that your employer or their witnesses say. While the standards for appropriate evidence sometimes have confusing legalistic names, they come from basic common sense.
Relevance: All evidence and testimony offered must have some relation to what the hearing is about.
For example, if you quit your job because your hours were cut in half and your employer starts to bring up the fact that you were late a couple times last month, that probably has nothing to do with why you quit, and is irrelevant.
You could say to the judge "Your Honor I don't see how this relates to why I quit," or you could just say that you object because of relevance.
Hearsay: Hearsay is testimony that is second-hand.
For example, if you were fired for supposedly stealing from the cash register and your employer brings a witness that can only testify that someone else told her that you stole, that is hearsay. The judge might find that your employer's story is not reliable because they did not bring the person accusing you to the hearing.
You can object to hearsay, but be aware that despite a preference for first-hand knowledge, judges will still allow hearsay to be heard. However, the judge cannot make a decision based solely on hearsay.
Asked and Answered: This just means that you've already been asked that question and provided an answer. Sometimes an employer will continue to ask you the same question over and over just to make a point they think will help them.
You can just say that you've been asked that question and answered it already.