In a lawsuit, the question will become "why do you park under the tree? This may be a difficult case to succeed in. You might consider a civil conversation with the neighbor to see if they would contribute to the trimming cost. Failing that, you should contact a local attorney to discuss the issue.
If you are talking about the New York Court of Appeals, you should ask your attorney if there is any possibility of a motion to reargue. However, it is pretty unlikley that such a motion would be grants unless there was some unusual reason for the Cout to want to reconsider its' own decision.
The Court of Appeals is the highest Court in New York. The only court left is the US Supreme Court. It is pretty rare that the Supreme Court agrees to take any case, but theoretically, it is the only...
One of the difficulties in dealing with insurance companies is that they often choose to believe the story that most benefits their position. In other words, if they can find a way out of paying, they will.
If the offending driver's insurance company will not reimburse you for the loss of your vehicle, you do have the right to your day in Court. Many times insurance companies will accept only a percentage of liability. They will reduce what they are willing to pay by that amount.
If you were rear-ended, you might be able to make direct claim against the person that hit you. Their own coverage should pay for the loss.
As to the value of the vehicle, most states now use a "fair market" valuation. It is certainly possible to find similar make, model and mileage with a higher pricetag in other parts of the country. Any arbitrator would likely use prices closer to your jurisdiction. You might try www.cars.com to find a list of cars like yours. It will not likely...
On its face, it sounds like a breach of the standard of care and therefore you theoretically have a case. But you haven't described any actual damages. Assuming you did wake up and you are fine now, there are no damages and thus no case. No harm no foul.
You should contact a Worker's Comp attorney in Buffalo to discuss exactly what happened and what harm it has caused.
There may be a state fund for people injured in situations where there is no comp insurance. Any Comp lawyer can advise you on this.