Has anyone ever made an observation that supports Lorenz shortening?

Answer 1

Yes, indirectly at least. Indirect evidence comes from the distance travelled by high-energy muons generated by cosmic rays in the upper atmosphere. They get much farther, to sea level, than they should in their lifetimes. In our frame of reference (on the Earth), this is explained by time dilation. But in the muons’ frame of reference, this happens because the distance is shortened.

For this and a recent direct test, see for example
http://renshaw.teleinc.com/papers/simiee2/simiee2.stm

Answer 2

No, not to my knowledge.
It seems quite unlikely that they ever will. The dilation in distance in the direction of travel as well as the slowing of time is derived to explain why the speed of light is exactly the same as measured by any observer - regardless of their constant velocity.
That simply means that the clocks and measuring rods will conform to the observer to give the exact same results that an observer at rest will get. There really can be no comparison between the two systems to discover which of them is "shortened" since both observers will get very legitimate and valid results.
The difference is referred to as the Lorentz Factor - and the difference accounts for the universal Constant of the speed of light for all reference systems.

Answer 3

Kinda. Check out Gravity Probe A, which confirmed Einsteins' theories of special relativity in respect to time - which pretty much confirms the length one as well. The results from Gravity Probe B, which measures the effects of frame-dragging, should be availible this summer.