What do nearby objects look like inside a supermassive black hole? This question is mostly about my lack of understanding of light cones, and how a light cone is manifested physically in a small, local region of space.
So I'm somewhere inside a black hole -- not spaghettified and still alive, but definitely past the event horizon.
My understanding is that all light will be moving in a direction toward the singularity (or rather that all directions are toward the singularity).
Were I facing directly away from the singularity as I fell in a straight line towards it, popular knowledge says that I would see the "outside" reduced to an ever smaller disk in front of me. Presumably some weird time stuff would happen and the light would intensify as well.
But if I fell straight in facing toward the black hole and holding an object directly in front of me (and assuming I'm not immediately destroyed by the black hole's photosphere), what would happen? Would it be redshifted until it disappears upon crossing the horizon? Can light travel back from the object toward my eyes but only on a small local scale (and long term, the light will end up in the singularity), would I ever observe the object crossing the horizon? Were I to turn around (could I turn around?) and look at the object and my arm from behind me, how distorted would it look?
 A: Just like the case without a black hole
Don't confuse spacetime "tilt" with spacetime curvature. On Earth's equator you don't worry about being turned upside down every 12 hours. Similarly, if you move very fast or approach a black hole space "rotates" into time and visa-versa, but any nearby objects you have rotate along with you and so look normal. Traveling very fast only allows <45 degrees of "tilt" since it's a Lorentz transformation that moves points along hyperbolas instead of circles; thus the light-speed limit. However, a black hole can "cheat" and rotate more than 45 degrees in a sense: inside a hole, your future is toward the center and you need a time machine to escape. Larger black holes accomplish this space-time tilting over a longer distance and so have less curvature (less tidal force) at the event horizon.
If you are inside a hole falling feet first you still see your feet. If a pulse of light leaves your feet it hits your head when your head is deeper in the hole than the feet were at the time the pulse was emitted. This is because "future" is toward the center, even for light directed away from the center. 
You notice nothing special at the horizon. Your future has gradually been tilted toward the hole as you have been approaching (falling from a great distance away for simplicity). You are doomed once the tilt exceeds your spaceship's rocket's/fueltank's ability to tilt it back. This will always happen outside of the horizon.
