Yes, Sony NS-WS623 is meant for the rough usage and it is both - waterproof and dustproof.
Hold down the button 1 for 3 seconds.
You will hear the startup sound.
When the Walkman turns on, the lamp (2) lights up.
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.
Yes, you can connect it with phone and talk and can use as a normal Bluetooth headset.