Good advice. Some locusts tend to suffer from limb die back. They are not generally long lived trees. The roots appearing at ground level is a characteristic of certain trees and is probably nothing to worry about, there is really nothing you can do about it anyway. You can identify the tree by how and what color it flowers, what the fruit/seeds look like and leaf shape. The tree will get fertilized as you fertilize the lawn around it.
After looking at the photo album more closely, I would guess it is a honey-locust. The bare limbs appear to be the ones that are being shaded out, and again, is a characteristic of the tree. It's probably ok, it's just not a strong, long lived tree.