Can I have public sex or engage in public sexual activity at the resort?

In short, yes. The resort culture has long allowed public sex in most areas of the resort, and if you go you will likely see people engaging in sexual activities. The resort culture and etiquette requires some discretion - for example you should avoid sexual activities in the dining areas, main "business" areas of the resort like the lobby, gift shop, etc., and near the water on the open beach near the docks obviously visible to boat and jet skis from neighboring resorts. 

The resort expressly allows sexual conduct around the nude pool and in the play room. Kinky Caribbean is a sex-positive event and all official Kinky Caribbean events are clothing optional to the extent the resort rules allow (for example, if the event is in an area of the resort where cover-up is required, then KC attendees must follow those rules.