못들려요 is more correct. 안들려요 is more like "i dont hear it" like you choose not to.
No, it's a passive verb so it's more like "it isn't heard" which is natural in Korean. Korean people also say 안 보여 for "I can't see".
Think of it more like "With respect to us, it is not heard." There's an implicit subject "it" the verb is acting on
In many cases yes using 안+ verb would mean like you choose not to, but this is an exception
I didn't know about this exception. Are there other verbs like that?