Friday is the most popular day to move home for two reasons. First of all, people like it because it allows them to unpack and settle in their new home without taking too much time off work.
The first priority should be items completed that week, such as safety issues, cleaning, unpacking, etc. Priority two should be tasks completed in the next two months, related to organization, maintenance and remaining unpacking.
All you need to do is wrap the delicate pieces in two or three layers. Plastic wrap or specially designed plastic sofa covers should be used to protect upholstered items.
You can move a house built on site if you really want to, but the expenses of moving a house often prevent people from doing so. What I'm really saying is that yes, you can move a modular house.