Counties and Building Names In Addresses

When Filling in an address for a retail building should the key addr:housename be used? Would it be better to use the building:name and leave that?

There is some overlap between the tags name= and addr:housename=. Usually you use name if the name refers to the organization/users of the building, and housename if the building itself has a special name - especially if that name is also used as the building's address. So housename might be appropriate in your case.

Also, what should the county be under addr:province, addr:state or something else like aadr:county?

Generally there's no need to fill in things like county, state etc.. These administrative areas usually exist as areas in the OSM data, so it's easy to calculate which one an address belongs to.

Normally it's enough to fill in addr:housenumber, addr:street and addr:postcode, the rest can be derived.