You don't need to listen for anything, but I can usually hear them peeping on day 20 and day 21 while they are in their shells. I think it's really sweet. They can peep because they have internally pipped at that point and are breathing the air in the air sac. Once they externally pip, you can can expect them to make it out of the shell with in 36 hours, though most can do it in 24 or less, one of mine only took 5 hours, but it's almost always longer than that.
Here's the basic process, they first internally pip. They break through the membrane into the air sac. They then rest for a while. Once the air sac gets low on oxygen, they realize they need to break through the shell so you can see an external pip, it's just a small set of cracks in the shell where the chick has broken through. They then rest again and start zipping. They turn around the shell breaking the shell with their beaks as they go so you can see a circle of cracks. They may rest again at this point, or they will jump ahead and push the 2 halves of shell apart. They will look very weak when they first come out, as the whole process takes a lot of energy. Leave them in the incubator until they are dry and fluffy, and only open the incubator once a day to take out dry chicks.
I haven't ever had a chick that has hatched on it's own die right after hatching. So I can't help you there. But I can for dry membranes. They happen when you open the incubater while others are pipping. When you open it, you let the humidity out so you should avoid doing so while there are external pips because without the high humidity, once pipped, the membrane can dry and stick the chick making it unable to hatch. If you notice the membrane around the chick looks white/yellow color then it's probably dried, all you have to do is take a Q-tip and wet it with warm water to gently wet the membrane. Note that there are 2 membranes, the one attached to the shell always looks white, but the membrane around the chick is transparent unless it has dried. If you don't open the incubator much, then you won't have to worry about this. Don't worry about leaving dry chicks in longer than a day, they won't need food or water for 3 days after they hatch, though I normally take them out once a day because they tend to knock other eggs around if I leave them.
If you need any other advice, feel free to say so.