My husband had bought me a car, with our savings account money (that was, also, making his car payments), but it was only registered in my name. When we separated, he told me that I could keep the car. I ended-up selling it a few days ago, and now he wants part of the money. Our divorce isn't finalized until March 25; does he get half the money for the car?

It depends.
The court will look at all assets, his car, your car, the savings account and all debts that you owe.
Normally each of you will get about half of the assets and half the debts.
Until the court orders you to pay him ( the court may or may not order this), no you do not legally need to pay him anything from the sale of the car.
You may ask him why he thinks you need to give him half, is he willing to sell his car and give you half?

It depends on whether or not you live in a community property state. Once divorce papers have been filed an automatic temporary restraining order goes into effect, prohibiting either party from selling any of the community property. It is referred to as a breach of fiduciary duty. Some judges may look at it as you completely disregarding their order. And unless there's a court order specifying that you can do these things it is contempt. For further information please see family code sections 721 (b) & 1101 (g) & (h). Please be careful these actions could result in a lot of trouble for you. My husband did it to me by selling the entire contents of our home and all of our family cars and keeping every profit.