From the Federal perspective (the National Register of Historic Places is part of the National Park Service), a property owner can do whatever they want with their property as long as there are no Federal monies attached to the property.
I think you probably mean the metaphor of piercing eyes, it means someone who has a really intense look in their eyes. Sometimes it could be that the colour of their eyes is quite different, like a really icy blue colour. piercing eyes are eyes that can see straight through a person. SUPP is right.
Unevenly set eyes convey an unique meaning. Firstly, the person is capable of seeing things from a different perspective and applying lateral thought processes to resolving problems. These people will analyse your comments and observations with a left-of-field mentality.