Perhaps a conversation about the matter with the mentor or with someone on the Mentoring Program Committee would be helpful. Each individual needs to examine his or her goals. If you want to pursue a specific goal, you would likely choose the mentee role. If you wish to pass on some of what you have learned to someone with less experience, you would fit into the mentor role. Yes, you probably do unless you are very new to the professional work world.
Most professionals have something they can teach almost anyone else.
On the mentoring application you have an opportunity to indicate the topics on which you would feel comfortable mentoring someone else. Not at all. Some employees with relatively few years of experience here have been successful mentors. One key question is how much you have learned in your time as an academic staff member. One possible disadvantage to this arrangement is that the mentees will have to share the mentor at events organized for program participants.