Geometric damping is also called radiation damping. It is defined as energy radiation into a surrounding medium. Damping is defined as energy dissipation property of structures and materials that are put through time-variable loading.
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Because of air damping.
Yes, but it involves a second order differential equation. Using the mass, spring constant and damping constant any physical object or assembly's damping ratio can be calculated. In the design of the vehicle the damping ratio was determined by the engineers at the automaker depending on the type of car. A sports car would have a higher damping ratio (maybe 0.7 or so) than a cushy luxury car. Over time the damping ratio will change as the components age. The most obvious is the bouncy feeling when you don't replace your struts or shocks as intended. That's when your tight sports car's suspension starts to behave like a 70's Buick. You just lowered your damping ratio without knowing it.
1/sq. root of gain
That all depends on what you mean by "form". If you are referring to "shape", then yes it can be geometric. For instance, a triangle is geometric.
"Geometric" means of, or referring to, geometry.