It's two times the propagation delay because the signal has to travel two times the cable length - down to the short, then the effects of the short have to propagate back.
The 1m length was chosen for being the nearest piece of coax I had lying around
The effect of the 50 ohm tees is minimal. It will cause a small impedance mismatch and a little bit of reflection, but not enough to skew the measurement. I tried 75 ohm and 50 ohm cable and a 200 ohm pair and couldn't get anything nasty out of that.
The setup is the same - look at the traces in that picture. The voltage across the shorted coax drops to zero after some ringing, meaning the impedance has dropped to zero (V=0, so V/I = R = 0).
Be warned that this is a bit of a fiddly experiment to do - the signal generator needs to output a clean pulse with a rise time a good bit faster than the propagation delay, or else it's hard to find a good spot to take the measurement from. The pulse generator I used here was barely good enough. And if the rise time is
too fast, the exact way it's set up becomes critical or else it will be set into a ringing fit. (I tried a
Jim Williams pulse generator and couldn't get anything coherent. I suspect much of the problem was related to the gross impedance mismatch around the sense resistor.)
Also, the resistor should have somewhat low inductance. I used metal film. Don't use wirewound or anything silly like that.