Hi fellow buckeye fan. You will love CSS. Been there 3 times and going again in Sept. Now to answer questions:
Delays with luggage is like any airport. Luck (or bad luck) of the draw. Only had one luggage problem which was last trip in 2011. Luggage missed connection in Charlotte, both going and returning. It did finally showed up. Pack swimwear in carryon.
On Tues and Fri. they have the beach party and gala.
The menus do change.
I would not want to rent a car. You will know after you see the drivers on the road. In the van we have had up to 5 coulples, also we were the only couple once. It depends on how many people arrive at the same time.
We have never walked off the property, no need as there is plenty to do. There are days when vendors are on property.
If this is your first trip to Jamaica, then do Dunn River Falls on a Sunday when there are no cruise ships in port. Also we enjoyed doing the zip lines. They have a desk in the lobby with off-site activies. Check it out to see what interests you. There are quite a few to choose from. They provide the transportation for these activities.
Do not miss getting a massage.
How do you know if there will be any cruise ships in port that day? (excellent tip btw)
You have gotten great advice here. The only thing I would add about the luggage is that at the airport, sometimes it takes a while to get through everything and to baggage claim, and they often don't let the bags continue riding around the belt, they often set them off to the side. So, don't panic if you don't see your bag riding around, look around for it.
At the resort, your luggage goes with you when they take you to your room.
There is a web site which shows when cruise ships are in port. I don't remember it, maybe someone can post it for you. Usually, Sat and Sun are not busy at Dunn's River as cruise ships are in home ports. When we went on a Sunday, it was our small group from Couples and one other, thus there was no rush going up the falls.