I can't answer all of your questions, but I've been to St. Kitts & Nevis once and can answer a few.

The Four Seasons beach is simply stunning. Nevis is a much quieter, less populated island than St. Kitts. The "capital" of the island is basically a very small village and somewhat picturesque, whereas Basseterre, the main city on St. Kitts (and the country's capital) is more grungy and unkempt.

If you stay on St. Kitts, you probably will need a car to get around, or else rely heavily on taxis. The main points of interest are scattered around the island and can be quite a drive away. There are local buses, but I don't think they're really geared to tourists. On Nevis, I think it's a pretty comfortable walk from the Four Seasons to the main town. Also, from what I remember of Nevis, it seems the type of place that you could comfortably bicycle around around; I'd assume there has to be someplace to rent a bike if you're so inclined.

The ferry between the two islands was quite pleasant, as I recall, but you'll have to plan your trips as there aren't that many sailings. Outside of that, I believe they have private boats that will take you, but I'd expect that to be quite expensive.