Those events all have specific needs to be met. The dying adventurer needs you to kill as many waves as possible in the time limit, at least 5 I think it is. If you do, they live and reward you. The ghost looking for something requires you to stay near it the whole time until the timer runs out, then you kill an elite mob and it has a happy ending finding what it wanted. The ghost being fed on requires you to kill certain mobs that contain its soul, you need to kill as many of them as possible before the timer runs out, the red timer bar will fill with a yellow tint as you do so. I haven't been able to complete this one yet.

I feel like the general theme of Diablo is that there are no happy endings anywhere, for anyone. The lore, the world, and pretty much ever quest feels this way. But that's always the way Diablo has been, right?

The events have success and failure endings.

Adventurers and traders/merchants in need: They thank you and leave if you manage to keep them / their merchant caravans alive.

Ghost whose soul being fed on monsters: He thanks you for knocking off all those monsters, takes the energy he collected, and turns into a lich(?) that you get to kill.

Or in nightmare dungeons where mobs explode etc, I'm unsure how to keep them from dying easily. :/

Most of the time when I run into those events, I wait for them to finish speaking (because our characters are super polite and cannot emote while others are speaking), then I say "no" and leave without doing them.

The only time I say yes is when they are saying "no no NO" or "it's so cold".