Is there any way to live stream audio from my Android phone via mobile internet network (broadband), so I could play the stream on VLC player?
Yes, there is an Application Camtest Audio. You can use it for streaming audio/video over the network using WI-FI. I uploaded my app for you in this link: http://www.droidbin.com/p1alrjvilfvl31joi1evm1qbilfl3
This app is based on an Open Source library called ["Libstreaming"]