Can a connection of HC-05 and Arduino Nano receive audio and display waveform on computer?
No, it can't.  The HC-05 is a Bluetooth Serial device, Bluetooth speakers are Bluetooth Audio Sink devices.

It's like asking "Can my bicycle fly?" 



I think you'll agree the answer is "NO".

The only possible way of doing it using the HC-05 is to receive the audio using your computer then pre-process it and send the important information to the Arduino through the HC-05, so the Arduino can then send it back to the computer for displaying.  But then, what really is the point of the Arduino...?!