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.