Which types of structural framing systems and materials are most commonly used in the US for residences? For office buildings?

What factors determine why these are the most used materials?

In the U.S. wood framing is most commonly used for framing residential buildings. This is a result of the long history of logging wood (a historically available resource throughout a significant portion of the U.S., as well as the relatively cheap cost of wood and its lightweight properties which make it more viable for transporting.

For office/commercial buildings, steel framing is the most common type of framing (although concrete is also very common). Steel and concrete have greater durability and strength than wood, so these are the materials that are needed when building buildings with more than a few stories high.

Why do different teams of designers and subcontractors link and share their models during the design process? 

What are the advantages of linking models?

Are there any disadvantages to linking models?

How do you think design coordination was done before we started using digital models? 

What advantages does doing this coordination digitally have over previous methods?

Before using digital models to coordinate design, I imagine coordination was done in person during regularly-scheduled meetings where every party brought their respective drawing sets and compared them to the other traits. When not in person, coordination probably happened asynchronously via markups on physical drawings and mail delivery. I suppose there was always a "baseline" design that all traits used to start from so that design work could be done simultaneously to some extent, and then the coordination meetings were used to identify and address conflicts.

What strategies can design teams use to find and avoid clashes prior to the start of construction? 

What can be done besides sharing the models digitally?

At what point in the project development process should design coordination start? 

Is it ever too early?

I don't think coordination can ever start too early from a theoretical standpoint. Even if there is only a very high level design and the input necessary from some of the traits is very little toward the beginning of the design process, it's always a good idea to coordinate and avoid conflicts in the design early rather than having to deal with larger conflicts later on. From a realistic and feasibility standpoint, the project owner or its representative likely prefers to not involve many parties in the design process until there is significantly more than a conceptual design since it costs money to have designers and engineers participate in the early design process when their input is likely small.