I think I understand that an analog audio sine wave has to coalesce to square PWM wave.
Yes.
Do not do any serial printing or floating point arithmetic in the loop because it slows down the sample rate to an extent that it will not be high enough to work. There is no need to convert the number into a voltage. You should see that 2.5 voltage change as you apply audio, if it does not change then it is either wired up wrong or you have not got a big enough input signal. Ideally you should get a swing between 20 and 1000 or so, if you see the full range of 0 to 1023 that means the audio is too loud and you are getting clipping which will distort the audio.
The analogue read returns a number between 0 and 1023, where as an analogue write accepts a number between 0 and 255. Give it a bigger number and it will just wrap round, that is it will just take the value of the least significant byte of the number you give it. So you must process what you receive by dividing it by four before you send it out, do this by shifting the value two places to the right with the shift operator >>
I do feel that this project is pushing the limits of your current knowledge and you are being hampered by your lack of fundamental knowledge of both what you need to do and how to do it.