You can check the charging status with the lamp ( 3 ).
While the battery is charging: orange when charging is complete: green
No. Sony NS-WS623 does not have FM radio.
Yes, you can connect it with phone and talk and can use as a normal Bluetooth headset.
No. It does not have remote control.
Yes, it does have fast charging. Charge it for just 3 minutes and it will work for another 60 minutes.