Does all light travel at the same speed in a vacuum and through other medium?
All light travels at the same speed in a vacuum as measured by an inertial reference frame. Light slows down when it travels thru a medium.
All true. However just to finish it up; photons still travel at c between absorption and emission by the medium. Which is, of course, just another way of saying that light and its quanta always travel at c in a vacuum.