Does Bluetooth LE stack supports A2DP profile?
Does Bluetooth LE stack supports A2DP profile (audio steaming)?


No, that is part of the classic spec only.


  if there is any dual mode stack which I could use in combination with BLE and classic stack


Probably, none come to mind though because I haven't researched dual-mode chips much.


  Also if anyone knows Android OS supports dual stack?


Generally yes if it has the silicon for it and you are on Android 4.3 or newer. My HTC One has had SDK-supported BLE as well as classic since Android 4.3.