No. It does not have remote control.
Yes, Sony NS-WS623 does have NFC connectivity option.
Sony WS623 comes with LED indicator. If it is not fully charged and require charging - it will show orange light and when it is fully charged - it will show green light.
Sony WS623 has 4GB internal memory and you can further expand it up to 16GB with the help of MicroSD card.
Yes, you can connect it with phone and talk and can use as a normal Bluetooth headset.