Question 1: Nirvana drivers... We've never used the drivers from the places we've stayed. We call Linston. Is it insulting to the 'hotel' drivers? I don't know. We love Linston.
Question 2: Nearest/safest ATM - we've always used Times Square but I defer to others who have more (recent) experience than I.
Question 3: Tons of places near Nirvana to eat and drink and I'm sure you'll get plenty of responses on that one. We go to Marshall (Step-A-Side) quite frequently. Bourbon Beach, Tony's Hut for drinks, Allan at the Tree House for jerk chicken/pork right on the beach.
Question 4: Supplies - we've always stopped at Sunshine Plaza in Negril - no particular reason, just because.
Question 5: There are a ton of great beach food vendors - Patrick the lobster guy comes to mind immediately - he'll (generally) be wearing a white shirt with lobsters all over it.
Question 6: You'll get mixed reviews on this one. We use it and love it! It's superfast, particularly when arriving on a Saturday. Last year our flight home was delayed for hours and it was terrific to be able to sit in the lounge and eat and drink.
Question 7: I wear my Oakleys - I'm aware that they might not make it home but it's a chance I take. And yes on the shorts/t-shirts/sandals question. I would strongly recommend bug spray but look forward to seeing what others have to say about what to bring.
Enjoy your trip!