No. It does not have remote control.
Yes, Sony NS-WS623 is meant for the rough usage and it is both - waterproof and dustproof.
You can check the charging status with the lamp ( 3 ).
While the battery is charging: orange when charging is complete: green
Sony NS-WS623 is quite light weight. It weighs just about 32 grams.
Yes, it does have fast charging. Charge it for just 3 minutes and it will work for another 60 minutes.