Since the dagger attack is already underway, I doubt your twitch response will be fast enough to stop the person who is in the act of stabbing you.
Now, people do get stabbed in the heart and live. So, no, while the damage would rather be extreme, if the target has sufficient HP, it doesn't have to be an insta-killl.
To the other issue, you use a lot of skills and proficiencies and 5E has no mechanic for training them all that get used.
And finally, not if the player made the call because their character had enough HP to know they would survive, then it would be "Ok, your character is dead. Happy?"
Case in point. In our session yesterday our PCs used Dimension Door to land on top of an adult red dragon that was flying over 60 ft above during the battle. After failing checks, or being knocked unconscious, some PCs fell from the dragon's back, taking 20d6 damage when they landed. Now, since most of the PCs have over 100 hp, the fall resulted in being knocked out (if not unconscious already) or a failed death save. These were not PCs taking the risks because the players metagamed. Since each time you go to 0 hp, you gain a level of exhaustion at our table, the battle ended with most of characters having 2-4 levels of exhaustion each. For the player whose PC had 4 levels, he was REALLY starting to sweat! We ended up using half-a-dozen Mass Cure Wounds spells, just to keep everyone from taking auto-failed death saves.
Anyway, the point is when players metagame, throw the mechanics out the window and narrate as you see fit. I see fit to say, "Ok, your character is dead. Happy?"