No. You can figure it out just from the license plate. The state database that contains that information is only available to police and DMV.

You can get it from your insurance company. It should be on your insurance card. IF you don't have your card with you then log on to your online insurance account or call and ask them to email you a copy.

Did you buy insurance for it? If you did, it should be free to replace it or get it fixed. If you didn't, then you'll have to buy a replacement frame.

Your health insurance might let you get a new pair if you haven't gotten new glasses recently.

you said after the incident, assuming the accident caused them to "fry" a good shop will look into it, but to be sure ask them to. remember you are & your insurance are paying them.

If I lived in Iowa I'd go to the the Iowa DMV website and search for registration/renewal fees. If I had more time now, I'd do it for you, but alas, I have too many automotive questions to read and answer.