False report of a crime is a crime, often a felony. False swearing can also be perjury which is a crime. The civil wrongs known as libel and slander can bring money damages.
propensity evidence is often not admissible in civil cout unless it rises to the level of a "habit". Couts are interested in facts not what might have happened based on prior conduct. For example, a history of speeding tickets doesnt prove speeding at a particular moment. Habit evidence is stronger and shows hat a person always does the same thing in a given set of circumstances.
The at fault driver's liability insurance should pay. Your own comprehensive/collision should cover it too.