As peaches mature look for brown, rotten areas. The fungus starts on immature fruit as a small circular brown spot, later enlarging, and ultimately rotting the fruit. Remove and destroy infected fruits and spray a fungicide such as sulfur.
You're probably seeing the work of voles, also known as meadow mice or meadow voles. They grow to about 7 inches and nest in shallow underground burrows, sometimes taking over abandoned mole tunnels. They usually feed at or just below ground level. Their favorite foods include bulbs, tender veggies, flowers, grass and bark.