Yes! You can derive this quite easily using the so-called raindrop coordinate system…
Yes! You can derive this quite easily using the so-called raindrop coordinate system (Gullstrand-Painleve) for a Schwarzschild style blackhole. For (b) what actually happens is you would see time accelerate outside the blackhole, so you wouldn’t see the entire future all at once. (Things also get compressed and warped in various ways, so it wouldn’t look like the night sky.) You can find youtube videos of what it looks like falling into a black hole with 360 degree views made by scientists who simulate what it looks like for things to fall into blackholes.