Modular homes, which are frequently confused with mobile homes, are designed and constructed to meet all applicable building codes, and are permitted in all residential zoning districts.
Basically, a modular home is exactly like a site built home except it is built off-site and transported to the site. It's plans would be approved before off-site construction just as a site built home would be. This is also defined in VA Code as such.
I participated in Green construction projects in Fairfax County using modular construction. These homes can be FAR better constructed than a site built home. It's an excellent choice.
This normally depends on whether the lot is in an already established neighborhood or not. The restrictive covenants for a neighborhood usually state what kind of home can or cannot be built there. In my experience, most established neighborhoods do not allow modulars, however, if the lot is not in a neighborhood you are probably fine. Also, there may be restrictions on what type of modular home. As you probably already know, there are several grades of modular homes. The lowest grade of these are built fairly cheaply. A high quality modular home often can be quite elaborate and even built better than site built homes. Hope this helps.