한국어로 뭐라고 해요? Do you want ''me'' to sing?
How can I ask someone ''Do you want ''ME'' to do something(verb) how would I write ''ME'' in the 문장.

너는 노래하고 싶어요? do you want to sing?
너는 ''나로'' 노래하고 싶어요? do you want me to sing??? is this right?
correct me if i'm wrong..

Question

한국어로 뭐라고 해요? Do you want ''me'' to sing?
How can I ask someone ''Do you want ''ME'' to do something(verb)  how would I write ''ME'' in the 문장.

너는 노래하고 싶어요? do you want to sing?
너는  ''나로'' 노래하고 싶어요? do you want me to sing??? is this right?
correct me if i'm wrong..

Answer

Do you want to sing? = 노래하고 싶어요? it will be natural to say..(because it will be question to some one in front of you,, so you don't have to say "너는")

Do you want me to sing? = 제가 노래하길 원하세요?/ 제가 노래하길 원하시나요?(존대)
                                            내가 노래하길 원하니?(약간 낮춤말, friendly)

Answer

Kyoungjoo, what you wrote is coloquial? 
I thought it would be something like : 노래하라고?

(Literaly, "노래하라고?" means "You asked me to sing?")

But I'm not a native, so we need one to check (maybe Kyoungjoo could do it?:)

Otherwise, what about "노래할까?" (kind of "should I sing?")