Somewhat oversimplified, but broadly correct. I'm familiar with general relativity and some black-hole physics, so I'm in a good position to judge.
Stellar evolution is much more complicated than what it described, but it would be hard to squeeze very much detail into a few frames. Maybe instead of just saying "hydrogen", say "hydrogen, then helium, then carbon and oxygen, then silicon and the like, then iron", but even that starts getting long-winded. Perhaps "hydrogen, then other materials, then iron."
It gets right that an infalling object observed from the outside would seem to take forever to reach the black hole's event horizon, as it's called. It would get very redshifted and dim over a timescale that's approximately the infall timescale at the event horizon, however. This is about 10 microseconds for a solar-mass black hole, and it is proportional to the object's mass.
The first and most straightforward possibility is falling into the black hole's singularity. It's called that because in classical-mechanics gravity, it's expected to be infinitely dense. However, collapse to it will run into quantum-gravitational effects at Planck size scales, about 10^(-35) m, and those aren't very well understood at all. In fact, quantum gravity in general isn't very well understood.
The second one, being shot out the other side, I haven't heard of, but it may be possible. An important question is how much an object would be squeezed as it passes through.
The third one, going through a wormhole, is rather intriguing, but there are two questions for using one to travel. Will it be stable? Will its tidal forces be tolerable? If a wormhole must be stabilized by quantum-gravitational effects, then it will have Planck size scales, meaning that
all structure of an object passing through will be crushed -- all macroscopic structure, all atomic structure, all nuclear structure, and all hadronic structure will be crushed out of existence.