I would reach out to your dad's insurance provider to see if you can be covered. They may be willing to cover the accident since the policy is still active. If you have any questions, feel free to ask.
Unless you were under the influence, drove recklessly, acted with intent, or fled the scene in a hit-and-run, I don't necessarily think you could be charged for a felony if you've been cooperative. However, a suit could be filed against you for damages. Regardless of both parties' insurance status, if you were at fault for the accident and the other party can prove this, then you need to pay for the damages caused.
If they are non-renewing for an unsigned app, you should be able to contact them and get that resolved. If you don't want to stay with them, I would still finish the term and move on to a different insurer.