Branching at full speed is probably not possible with the Hyperloop as designed; the skis are curved to match the diameter of the tube, with a ~1mm clearance with the tube surface, so there is no passive tube design that could accommodate a "switch". In order to continue from Section A to either Section B or Section C, you'd have to make an intermediate length of tube several hundred meters long that could be physically moved at one end from B to C, with sub-millimeter precision
Wait, meaning that while it's technically possible, but it'd be really tricky to accomplish? Gee, I wish I had written something like "Branching would be really tricky, but there's no physical barriers" at the top of my post ;)
The reason is threefold: drag continues to increase at higher speeds regardless of the speed of sound
Drag is reduced in the first place by using hydrogen even at a given pressure. And you can use 1/4th the pressure and still maintain lift because you're moving four times as fast. And given how few reboosts are needed from LA to SF in the base case, a few more per unit distance hardly seems limiting.
If you consider that the steel Hyperloop pipe draped across 30m-spaced pylons will approximate a vertical sine wave, then at 700mph the allowable sag is only about 5cm
Irrelevant because earthquakes impose far more deflection that you have to be able to counter (and that the proposal calls for countering) than a craft moving past.
Mechanical braking from 1500mph in the event of an emergency is also a non-starter
What, you're picturing drum brakes or something? You're moving at high speeds in a giant steel tube. Magnetic braking couldn't possibly be easier.
a 700mph capsule will incur about 2g's of aerobraking deceleration
Where are you getting this from? Even if the tube was instantly full pressure (which it wouldn't be), a streamlined shape will not experience 2Gs at 700mph, any more than a passenger jet losing full engine power does. And anyway, 10g horizontal is not fatal even if that was the case. The average untrained individual, properly restrained, can tolerate 10g for a minute without even loss of cognitive function.