how come the parachute does not get tangled up?
It could be that the centripetal force and the air resistance inside the parachute keeps it from tangling.
Maybe. But even spinning around a horizontal axis would not entangle the rope, if it attaches to a point on that axis at the circumference. Just like a gyro spinning around an horizontal axis, which is supported by a rope on just one side.perspective. it looks it is spining horizontal but it´s already vertical.