None of what you described typically causes death. They can cause serious injuries, but rarely death.
It's not possible for a palm strike to the nose to break off the bone and drive it into the brain. That's a complete myth. There's no truth to it whatsoever. If anything, the bone will shatter into bits or will break in two. It won't get driven back towards the brain.
A knife-hand strike to the side of the neck is a common strike in martial arts of all kinds for one reason: It causes people to faint. There are many videos showing examples of this on youtube.
What's happening is that the Vagus nerve is being given a whack, and the Vagus nerve is what measures blood pressure going through the major arteries of the neck. If it is struck, it will send the brain a signal that the blood pressure is way too high. So the brain responds with a signal telling the body to dramatically lower the blood pressure. Since the blood pressure wasn't actually high to begin with (it was just a glitch caused by the strike to the neck), blood pressure suddenly drops so low that it causes the brain to faint.
It has been known to cause death in rare cases when someone suffers a stroke because of it. Not only is it rare, but because the stroke can occur up to days after the impact, this technique can't be used reliably for the purpose of killing someone on the spot.
Strikes to the arteries in the neck sometimes dislodge arterial plaques on the inside of the arteries, especially in older people who have more plaque build-up in their arteries. This plaque then travels up into the brain and clogs the smaller blood vessels inside of the brain. That causes a stroke which can lead to death.
Strokes can also be caused by tears in the arteries of the neck which then causes blood clots. The blood clots become dislodged and travel to the brain, where they clog smaller blood vessels in the brain. And that causes a stroke.
It's rare that we see this happen in martial arts today or as a result of real fighting. Part of the reason is that it's rare to find anyone able to successfully perform a knife chop to the neck on someone who is moving around and able to block it or flinch out of the way. It turns out it's a lot harder to do than martial arts practice would suggest.
This is more frequently documented as a side-effect of Chiropractic neck manipulation. Chiropractors perform a sudden twist of the neck. It's a bad idea, because that procedure has a significant risk of tearing the arteries of the neck and causing strokes. Don't let anyone try it on you.
Some people suggest the knife-hand chop to the side of the neck is actually severing the nerves of the spine or is breaking the spine itself. The muscles and tendons of the neck provide a great deal of resistance to any strikes from the side. That alone would diffuse the force of the strike enough so that it couldn't break any bones of the spine.
Beyond that, the head and neck aren't really held in place. It's like hitting a speed bag. The head will move. So the neck won't receive the full force of the strike.
The vertebrae of the neck are mostly immune to this kind of a strike, also. It's almost impossible to break the spine with a strike of any kind. That's because of evolution. The way the spine is shaped makes it really hard to break using a strike of any kind. It usually requires a weapon of some sort.
About the only way you could damage the nerves of the spine would be to attack an area of the spine that is closer to the surface and therefore less protected. You could hit the back of the neck or the top of the shoulder. You wouldn't break the vertebrae this way, but you could cause an injury to the nerves, which could cause death.
Attacking the neck can also cause the head to bob. If it's done very quickly and with a lot of force, it's possible the head could snap some bones of the spine. And that could cause death. It relies on a completely relaxed neck, which is almost never the case in a real fight. We don't really see this happening at all in any street fights or professional fighting.
Just to reiterate, knife-hand strikes to the side of the neck rarely cause death. And it can't be used reliably for that purpose. When death occurs because of this strike, it's usually unpredictable and often caused by a stroke later on.
As for the temple, it hurts to get hit there, and it can result in a knock-out or a concussion, but not usually death.
One of the things to keep in mind is that a lot of martial arts "knowledge" has been passed down from generation to generation. Some of it may have been based on a misunderstanding of what was actually observed. Some of it is exaggeration (usually for marketing purposes). Most of it is just plain myth.
As for stuff based on real observations, something may have been seen as the cause of death. But was it the sole cause of death, or were there other factors? Like in the case I mentioned above where a knife-hand strike happened to kill a guy, it wasn't because the strike broke the neck or something. It was because it dislodged some plaque and caused a stroke. But again, that's not a common outcome.
And another thing to realize is that these arts come from times before modern medical science. Back then, it's possible for a palm strike to the nose to actually cause death. It wouldn't have been from pushing the nasal bone back into the brain as people may have thought back then. Instead, it could be due to a simple concussion or some other head trauma which is easily diagnosed and treated nowadays.
I'm just glad you didn't mention dim-mak, the so-called "death touch" or "delayed death touch". That's a whole discussion in and of itself. And I would tell you it's basically all myth and misunderstanding, just like above.
Many martial artists end up chasing these "amazingly powerful if true" kinds of things only to realize it's basically a myth and a waste of time. I spent quite a bit of time studying dim-mak and acupuncture, for example, and I can honestly say it was a waste of time and a red herring. Don't bother.
Lastly, I just want to say that fighting of any sort can cause death, often in unintended ways. Head trauma can still be deadly in modern times. Just punching someone in the face or head can kill them. It happens. Blood clots happen and can kill.
People sometimes go back home after a fight, get a headache, take an aspirin, and go to bed. They don't realize it's something serious, so they don't go see a doctor. Some don't wake up after going to bed. So, always get yourself checked out by a doctor if you ever get into a fight, especially if you got hit in the head.
Hope that helps.