Branching would be really tricky, but there's no physical barriers. Note that even Musk's proposal isn't as far as you can take the concept. If you fill the tube with very low pressure water vapor instead of very low pressure air (via more pumping to overwhelm leaks, plus water vapor injection), your top speed jumps 40%. Fill it with hydrogen and it jumps 300% (normally hydrogen is a real pain to work with due to flammability, embrittlement, etc, but the densities in question are so low that such issues are mostly avoided). So we're talking the potential for hyperloop "speedways" for long distance runs that could blow airplanes out of the water.
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, with the entire thing enclosed in vacuum. By the time demand is great enough to warrant branches, it's probably more cost-effective to make a dedicated parallel tube than to re-purpose a single tube with a ridiculously complicated switch.
Hydrogen (or water vapor) would be most helpful in reducing Kantrowitz effects near the sound barrier, but not necessarily in enabling higher absolute speeds. The reason is threefold: drag continues to increase at higher speeds regardless of the speed of sound, lateral acceleration increases with the square of velocity, and the vertical precision of the pipe also improves with the square of the velocity. 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 between pylons before the capsule's vertical suspension is overwhelmed and it starts "bouncing". (Assuming the mass of the skis/suspension is 10% of the capsule mass, so it can accelerate vertically at 10g to keep contact with the track.) At 1500mph, the tube requires a vertical precision of 1cm between 30m-spaced pylons, and its trajectory would have to be ridiculously straight to avoid problematic lateral g-forces. Mechanical braking from 1500mph in the event of an emergency is also a non-starter; 700mph is right at the edge of what can be feasibly done without melting brakes or destroying the tube. And in the event of a rapid tube repressurization, a 700mph capsule will incur about 2g's of aerobraking deceleration; at 1500mph it would experience about 10g's, likely enough to destroy the capsule and/or kill the passengers.