USFS doesn't want people attempting figure skating stuff in blades that aren't meant for figure skating. Flat = speed skater.
USFS allows flat, as you pointed out in an earlier response. Maybe it is good for school figures and skating skills? Some skaters go so long between sharpening that maybe they go slightly convex.
Concave = unable to skate on edges, which is what figure skating depends on. Also, have you seen anyone try to skate with a concave?
I assume you mean convex.
If someone sharpened figure skating blades convex with a narrow angle like a kitchen knife, I bet they would sink into the ice until they stopped.
But maybe there would be other shapes, like concave with a thin convex line down the middle, that would achieve something.
Blades with circular toe picks? That seems to me designed to cause faceplants. Toe picks are sharp for very specific reasons; namely, to assist with those jumps and spins.
Perhaps that would depend on how small the circle was, and how sharp the angle. E.g., if it had a sphere bottom shape, it would help prevent traveling while spinning. Perhaps there are other shapes that might be better in some ways.
As for blade technology, people are working on similar things. All that stuff you listed isn't illegal, but the technology is not there for wide implementation - or is downright impossible without making skates too heavy to wear. Related, check out Blade Science: https://www.blade.science
Fascinating. But I would consider it cheating to build springs, solenoids, motors, or equivalent into boots or blades so you could jump higher, or skate or spin faster. But they are mostly talking about damping landings, to reduce injury.
There are augmented reality programs out there.
There is a difference between using aids for training, and using them to overcome memory or control problems during a test or competition - e.g., imagine being able to see the dance pattern you are trying to follow (or hearing tones that tell you to move left or right). I would consider that cheating too. Or hearing coach feedback, without judges' knowledge. Or music without reverb.
Battery heated hockey blades, to reduce friction, never became popular. I don't know whether that was due to excess weight, or a reduced ability to push and stop.