Regarding Rose on the screens in Series 4, I think the TARDIS screen is easier to rationalise than the Midnight bus one, but I like to think it mirrors what happens in Doomsday. Rose is somehow projecting an image of herself (with parallel UNIT or Torchwood's help) much like the Doctor did on the beach. Except that whenever she latches on to where the Doctor may be, she just misses him.
Also, Rose could've just recorded herself shouting for the Doctor and is chucking it out through time and space via whatever technology is available. Kinda like how everyone uses phone signals to reach the Doctor in the finale; maybe there were more instances of screens around the Doctor flashing up with Rose that we just never got to see. I kinda like that headcanon now actually! xD
Yeah, most likely something like that. I mean, Rose was working for parallel Torchwood, right? Who knows what kinds of gadgets they had.
That remind me, there’s one question I always have about Pete’s World: do Time Lords exist there? Does the Doctor exist? Was there a Time War? Is there Gallifreyan tech that Rose could salvage? So many questions. Gah, I wish RTD had gone through with that Rose Tyler spinoff to flesh that out a bit.
