No. It does not have remote control.
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.
Yes, it does have fast charging. Charge it for just 3 minutes and it will work for another 60 minutes.
You can check the charging status with the lamp ( 3 ).
While the battery is charging: orange when charging is complete: green