Your compost pile has most likely thawed to the point where you can turn it. If you saved some leaves from last fall, add another layer. This will help balance out your nitrogen rich additions with some carbon and get your compost pile "cooking" again.
No. It is too early. Even though the temperatures have been unusually warm, there is still a chance that we can experience an extended peered of frost. Fertilizing will only encourage new growth that could be overly damaged by those frosts. Hang tight and wait!