If the water is lower than your temperature enough to be acting as a coolant, then no; if it's not cool enough to do that, then yes.
I don't think so. In addition to what Jiku Neon said, about 30% of our waste is excreted through our skin. So, if for some reason, you are just a little too salty today, you could go sweat it off at the pool.
I swim, yeah you probably do sweat when you swim, but you don't feel it because your in the water. After bring in the water for like 1/2 hour your skin goes wrinkly though too.
Well. This thread has put me off swimming even more now. ew @ swimming around in other people's sweat .-.