1. It is arbitrary chosen value, constrained by manufacturing process and lines placement. Probably via in the center is forming t-junction from 50 Ohm line on the other side of substrate.
2. They can't continue divide 100 Ohm line with t-junctions, because it will result in 200 Ohm lines, which may be too thin to manufacture. So before each new T-junction they lower impedance from 100 Ohm to 50 Ohm with Sqrt(50*100)≈70 Ohm. Point after 70 Ohm line is 50 Ohm virtual impedance point, which is immediately divided to two 100 Ohm lines
3. I do not know, but butler matrix is too big and requires more RF hardware
4. Not difficult, especially with help of computer simulation.