Hey Mark, great questions! I'm not a chemist nor biologist, but here's how I understand it from what I've read.
Common table salt is by definition sodium chloride. That's sodium ions ionically bonded to chloride ions. So it's correct to say that there is no salt in seawater because these ions simply don't stay together to form salt crystals when they are in water--except maybe for a few seconds when salt crystals lying on the shore have just been washed into the water and have not yet have had time to dissolve.
It's sort of like there isn't paper in a bonfire. Sure, you can throw a sheet of paper into a fire, but it won't stay paper for longer than a second or two. In much the same way, you can throw salt crystals into water, but they just won't stay salt for long.
Also take into account that the sodium ions and chloride ions dissolved in water do not necessarily have to bond with each other again to form table salt (sodium chloride). They can just as well bond with all sorts of other elements. For instance, the same sodium ion that was part of a salt crystal can not only turn around and bond with a water molecule, but it can also bond with all sorts of other ions to form sodium fluoride, sodium bromide, sodium iodide, sodium sulfate, sodium bicarbonate, sodium carbonate, etc.
As to the buoyancy of saltwater, you got it exactly right. Saltwater is indeed denser than freshwater and so, when a person gets into seawater, the water they displace creates, according to Archimedes' principle, a buoyant force that is greater in magnitude than if they had been displacing an equal amount of freshwater. So saltwater, being, heavier than freshwater, creates a bigger upward force when you swim in it.
Regarding fish dehydrating in saltwater, that's actually exactly what happens if you drop a freshwater fish from a river or lake into the sea--the water in their bodies is sucked out of them. But it doesn't happen to saltwater fish because they're continuously excreting the salt that gets into them. This is called osmoregulation. So it's not that they have the same mineral concentration in their bodies as the water that surrounds them. Instead, they pump salt out of their bodies all the time, doing so mostly through their gills.
