In reply to the first part of your question re the black band - haven't a clue, I fly the A319 which doesn't have one and I'm not aware of very many types which do.
In answer to the second part re different radar displays on each side of the flight deck, most systems will allow it with the radar display being superimposed over the map with the relevant scale selected. When the radar sweeps one way, it looks in the direction selected by the guy (or gal) on the left (ie 5 deg UP) and the other way looks in the direction selected by the person on the right.
There's probably a much simpler way of describing it.