10.Does the BTR5 support idle time power off?

Yes, it supports idle time power off for saving power. When it's connected to other devices, it will enter standby mode  if no music playing. Its battery life is about 300 hours in idle time.

When it's not connected, it will power off automatically after 2 minutes.(You could set the idle power off time via the FiiO Music/FiiO Control APP)

How to set idle power off timer for BTR5: