I noticed nobody has responded to your post yet. Have you posted this question on other Virgin Islands' forums? If not, try googling for other forums.

I can answer your questions,

Flexible hours, not usually.
Vary, usually outside labor or office
Mosquitos depend on rain
Unbearable? Depends on what you are used to, VERY hot and lots of stairs, if you aren't physically able to handle, let them know before you arrive.
Great people, great opportunity to have extended stay in VI, would do it again.

Make sure you budget for your stay, accommodations included but nothing else. Everything is expensive on St John, plan accordingly.

Good Luck