No. Sony WS623 comes with non-removable battery.
Yes, you will get a pair of normal earbuds and a pair of swimming earbuds.
Yes, Sony NS-WS623 is meant for the rough usage and it is both - waterproof and dustproof.
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.
No. It does not have remote control.