Answer: The surface roots are natural and should not be covered, so you do not need to worry about that. Any fertilizing would be done on the basis of soil tests indicating a need for additional nutrients. If the tree is in the middle of a lawn area for instance it most likely would not need any additional fertilizer. But a soil test is the only way to know for sure.
The tree itself, however, may be in danger. There are numerous bacterial and fungal diseases as well as borer insects that can attack cherry trees and they are often fairly short lived as a result. A main symptom would be darkened spots on the bark, also possibly sap or stickiness or sometimes holes in the trunk, and that overall "looking poorly" condition or decline.
I would strongly suggest you consult with your local county extension and/or on site with a professionally trained and certified arborist with experience working on ornamental trees for a more specific diagnosis and based on knowing that, deciding if anything can be done for the tree. They can also assist you in soil testing and determining whether or not fertilizer would be at all helpful in this case.
I'm sorry I can't be more encouraging.
Q&A Library Searching Tips