Another related question: What does the world (the outside of the black hole, the universe) look like to an observer crossing the EH?[/QUOTE]
The universe from just inside the EH looks pretty much like the universe looked when the observer was just outside the EH which follows from the frequent claim that an observer will see nothing remarkable at the EH. There is no sudden change. It is also often claimed that a falling observer will see the whole future of the universe evolve as he falls through the EH but that is not true.
Light rays are blue shifted as they fall towards the EH from the point of view of an observer that is static with respect to the black hole, but in the case of a free falling observer there will be an additional Doppler shift due to his falling motion away from the source, but I am not sure if that is enough to change the blue shift into a red shift. So redder or bluer?