Driver, I looked at these links and have several comments.
The first one seems to be falling upward, but at a fairly slow rate. I could certainly cause such a problem for the cameras. When it finally stopped, the phone fell off the hook and a ceiling plastic fell out. Whoopee!!! I'm not sure this was even a commercial elevator. It looked like a LULA or a residential, maybe.
The second one is harder to comment on. Lots of people claim a free-fall and actually experience a lock clip at speed and assume a free-fall. In the picture, there were definitely some broken cables, but the elevator pictured looked older and different than the one first pictured, They didn't back away quitte far enough to compare jambs, but I think I have seen that picture in somebodies video travel journal.
The third one has happened lots of times, mostly with Ward-Leonard systems and failed brake systems. These problems were what prompted the rope brakes, sheave brakes, and redundant braking systems.
In summary, you took three unrelated scenarios and tried to weave them into a workable possibility. I'm not even convinced that at least one of these links wasn't staged. I set up several scenes for movies and made elevators do things they would not ordinarily do. Would have required multiple simultaneous failures.

Go to the forum list, Safety talk, and find too dangerous and machine goes flying. Imagine somebody taping those from a different vantage point and then post them as happening in normal operation.

Essentially...yes.
Assuming those scenarios were real, I didn't think my scenario would be too far fetched if those elements were incorporated in one sequence and then some...

I'm sure that everything could be staged for the cameras (I'm assuming you are referring to the first youtube link), but I would have to question the motives, as there is not much if anything to be be gained by doing this...
Sure it could be a prank, but those 2 people getting out while the elevator moved would definitely gamble with their life in order to film this, especially one of them being a kid...
Suppose that could be fake too, but now it would be getting too elaborate for such a low quality video I think?...

As far as the teen free falling 5 stories in Bronx, there were several pics on the internet from different news sources, most showing the elevator cabin resting below the ground level, which looks like the actual elevator pit?.
Im assuming, if the emergency brakes have deployed, the elevator cab wouldn't have fallen that far down?
Of course I do realize, that when it comes to the news they like to recycle and re-use certain images, since most people wouldn't be able to tell the difference...
For example I have seen a news image recently titled "Ukrainian troops are moving closer to the border", while the image shown was taken from the NATO war in Kosovo some 15 years ago...(bunch of guys in fatiques marching somewhere, most people will not analyze it)...

Having said that, I think that I do have an above average BS detector as well, but to be honest I really don't think that the first video link was staged...

Essentially your scenario includes many factors that need to happen consecutively. The most catastrophic failure is the snapping of a brake shaft on a geared machine which I have never heard or seen happen. If this happened then the stopping of the car in the up direction is unlikely as safety gear is generally only operable in the down direction. Having said that newer MRL safeties are now bi directional. This is why you engineer to specs(hopefully) and incredibly rare if at all. Un intentional movement can happen. We had a car take off from the top floor into the top of the shaft(before my time) and I think an issue was created when the main contactor in the loop circuit flex earthed down enough to create a dynamic braking situation that had enough of a potential difference to create a current to move the car. I don't know enough of the situation to comment further but this is the only thing I ever heard of that was similar to what your asking.

@uppo72, thank you for taking time to read my thread.
Speaking of electrical glitches, I actually have a question about one:
I recall once someone once told me, that they know a person whom was traveling up in a highrise building, when to their horror suddenly the numbers on the display (not sure what kind) have reset themselves half way up and started counting from the ground floor again, despite being somewhere around 15-th floor or so with only some 6 floors to go before the top...
Supposedly the cab crashed into the top pretty hard, then cam down one floor and the door opened so this person was able to bolt out of it, presumably needing a new set of underwear....
Could this somehow happen, or was I a victim of an urban legend?...

I know of instances when a car went into the overhead and crashed, the car got stuck in the overhead, car safties applied.
This must be somthing that you are really trying to get the answer you want and won't let it go. That car would not have recovered in that instance, and yes there would be new skivies involved. Use your BS detector. The car would not have lowered if the case was that it slipped traction in the up direction. If it was overspeeding in the up direction most likley it would have tripped the overspeed switch on the governor, top final, both of which is in the safety circuit. 21 is not a highrise.

Ok...If I still remember the jist of this story correctly, there was no slipping traction, or overspeed involved in that particular case...
The whole plot revolved around the fact that the numbers on the floor counting-off display have somehow reset themselves, while the elevator was traveling in the upwards direction and started counting back from the ground floor, when in fact it was already passing a much higher floor...
In this story/legend, the elevator was simply confused at which floor it really was, so if it were a 21 storey building and the counter has reset back to 0 around 15-th floor this would mean that there were only 6 more floors available, while the elevator would somehow "think", that it still has the full 21 floors to go...

At the extreme end of nomal travel in both directions safety circuit stops the car, and will not restart with ELEVATOR tech reseting, regardless of what the PI says.

Thank you..this is the answer I was looking for, as far as this story is concerned.
Obviously an urban legend of sorts...

Your example is not uncommon. I would also suggest don't get caught up on superlatives like 'crashed' as it is incorrect and places a slant on the typical write ups from journo's to paint a picture of a lack of safety in lifts. What happened most likely, is the lift got what we call out of step. This happens sometimes but in NO WAY is the lift now UNSAFE. The lift will then continue in the up direction until in performs a CONTROLLED slow down into the top floor via the emergency terminal stopping. The reason why it 'seems' like it crashes is because the slowdown is done within a certain distance and has to be done quickly.

Thank you uppo72....Is there a building code on how much space there has to be between the elevator cab's roof and and the ceiling of the shaft once the elevator is sitting at the very top floor, or does it vary from building to building?

When your counterweight is fully buffered out there has tp be enough room for the top of the cab not to hit any of the deflector sheaves in the overhead. Every building is different I've had buildings with huge overheads and then none at all.