While you are not required to call the police for an accident (though it is generally better to do so), you do need to report it to your insurance...

Can I be sued by the owner of the car if the accident was my fault?

If your fault resulted in damage/total loss to the vehicle, yes, you may be held accountable for the loss. However, there are a couple of options...

Can I appeal a verdict in a personal injury case?

Appeals are possible, provided you have proper grounds. Simply being dissatisfied with the outcome is not sufficient. Usually, you must establish...