What is the right of the second party over the first party, concerning the damage to their car and the random shooting at it, if they swear an oath and are acquitted of the charge of injuring their brother?

The reference for disputes in this regard is the rule: "The burden of proof is on the claimant, and the oath is on the one who denies." If the first party does not have proof that the second party is the one who fired the shot that hit their brother, and the second party swears that they did not fire it, then they are absolved, and nothing is due from them. However, the first party is obligated to pay compensation for the damage caused to the second party's car, by paying the difference between the car's value undamaged and damaged. As for indiscriminate shooting, it does not result in a financial right unless it causes material harm.