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

There are many factors that can go into deciding the structural system of a building. Wood framing is typical cheapest for smaller construction projects. Steel and concrete (and hybrids of the two) are typically used once buildings get taller than about five stories. Steel is great in tension and concrete is great in compression, so depending on the demands of the structure different materials can be used more effectively. Other things to consider are location and proximity to the material manufacturing locations, environmental impacts, availability, construction expertise and more.

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

Coordination and collaboration is key when design projects get complex. Properly linking and sharing information can lead to less conflicts at the end of the day. The major advantage is being able to see which parts of the differing models conflict with each other. Another major advantage is the communication that can occur due to the issue assignment. This leads to simpler and more efficient conflict handling. A disadvantage could be the clutter and complexity of the project might be difficult to sort through.

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

It is never too early to start design coordination. As soon as anybody puts something on paper or into a model the coordination can begin. The quicker information is shared the quicker each designer can begin modeling. There may be a potential to start too early if the massing of the site is very volatile. However, as long as it is communicated that the massing is volatile, then the other designers know not to dive too deeply into their work, but can still begin contemplating high level design decisions.