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
Yes, you will get a pair of normal earbuds and a pair of swimming earbuds.
No. It does not have remote control.
Sony WS623 has 4GB internal memory and you can further expand it up to 16GB with the help of MicroSD card.