I understand that 「聞きます」 is he polite form and 「聞く」 is casual, but I don't understand how the volitional form 「聞こえる」 is also translating to "to hear~" and not "I will" or "let's hear" or "I think I hear" etc.
I think that even though 聞こえる literally means something like "to be heard", that isn't really natural English so is generally translated to be transitive. For example, even though「猫は聞こえる」would literally mean "the cat is heard" or "the cat is audible", it sounds kind of weird in English, so "I hear the cat" etc. is preferable.
Edit: I read the question kind of quickly, and I think I misunderstood what was asked. Hopefully this explanation was still of some use to you.
These verb pairs are sometimes called active-passive pairs, although that terminology is probably not on very solid ground. If it helps, great; if it’s confusing, ignore it.
Hopefully this explanation was still of some use to you.
