O, I think I understand your question better now :) 들려줘서 고마워 means thanks for letting me hear (for example a song), 불러줘서 고마워 means thanks for calling me/singing (a song) for me (here, if its meant as singing, it should be clear from the context that one is talking about a song, and not just someone calling you), 노래해줘서 고마워 always means thanks for singing. 부르다 is used instead of 노래하다 when it is clear from the context that we are talking about a song and it thus is unnecessary to mention this again.

I'm not sure what you mean with those endings (줘서), but 들리다 means to let hear, 부르다 means to yell/sing/call out, and 노래하다 means to sing. The difference between 부르다 and 노래하다 in the meaning of singing lies in context i think. For example, one can say 나는 노래한다 or 나는 노래를 부른다. Here, the first one means 'I sing' while in the second one 노래 is a noun, and the sentence reads 'I sing a song'. So it depends on if you want 노래 to be a verb or a noun.