Yes, I have measured a few and normally use the Stereophile or Soundstage measurements - IMHO one the every few useful amplifier measurements, as well as idle power, that tells me wow much I will suffer during hot summer days.

For curious people the other nice measurement IMHO is input impedance.
BTW, there are different techniques for measuring output impedance that will result in different values.
Yes, I usually email them to ask or confirm. They are very helpful and friendly concerning in this aspect.
Most SS amplifiers have high damping factor - output impedance less than or around 0.1 ohm. A few have around 0.3 ohm. My cables are still tuned for the ARC REF 750 - a tube amplifier with exceptional low impedance for tubes at 0.5 ohm.
No, IMHO they are "energy" controls, but properly used do not affect tone. On the contrary, comparisons show that some other cables are real "tone controls".