I know if you're too close, everything gets distorted, but I would have thought they look the same from any direction or angle, never managed to grasp the concept.
Maybe there is some 3d sim to explain this?
If the black hole is spinning, it has poles. We expect all black holes to be spinning. This is a subtle change in the shadow itself, but...
And if the accretion disk and black hole have misaligned poles, there should be a huge warp in the disk close to the black hole as the black hole frame-drags the accretion disk.
What happens at the singularity in a rotating black hole depends on your quantum theory of gravity. Some theories have the singularity as a "ring" instead of a point. I believe loop quantum gravity has a "planck star" in the center of a black hole.
Macroscopically, rotating black holes can be thought of as rotating the space around the event horizon. So the spacetime curvature doesn't just pull you directly to the center, there's an angular aspect as well.
Anyway, we are not seeing the black hole (because it looks just like a black circle in front of a black background). The interesting part of the image is a disk of material spinning around it. There is a nice 3d cardboard simulation and clear explanation in a video by Veritasium https://www.youtube.com/watch?v=zUyH3XhpLTo