If you both have insurance, your insurance is the primary policy and will cover the claim. Because you were not driving, it should not change your rates. If she is excluded driver under your policy, then your insurance will not cover. If the damages is greater than your property damage limits, then her insurance will pick up the excess.
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There is no mechanism to "remove" a judgment. However, if you have paid the judgment in full you can file a notice of satisfaction of judgment which will improve your credit rating as well.
If the Defendant is represented by counsel, the discovery request - interrogatories must be served on counsel for the defendant and any other parties/counsel who have appeared in the matter. If they are not answered within the time period allowed by law (30 days if personally served or 35 if served by mail) then you can make a motion to the court compelling them to answer the interrogatories. You can not serve interrogatories on non-parties. You can serve a deposition subpoena requiring them...
I am not sure from the information that you provided us that the school is not at fault. I think any of us would need more information to adequately answer your questions with a yes or no response. I would consult an attorney who can evaluate your case after providing more information and conducting some initial investigation. What is more, you need to be very care to act quickly as there as some strict time lines in filing a lawsuit. Good luck.