I was there 6 weeks ago. During the day I would wear either a sundress or shorts with top or t-shirt, and in the evening always a short dress or a short playsuit. I didn't take any heels but I did want to dress up in the evenings (the whole point, surely!) and I found that if I hadn't gone back to my hotel and changed by about 7pm I started to feel self conscious as everyone else was dressed up for going out by then.
I do think where you are staying makes a difference though, in terms of the dressed-up-ness.
I feel the cold and took a cardigan, but I never wore it, it was fine. But maybe the aircon will be colder in high summer 
For 3) have a look here - sorry don't know your budget and shape etc.
For 4) I didn't go to any beach clubs but you will be bombarded by ads for Drai's beach club when you get there, it's the newest one and did look fantastic.
Have fun :)