Such things do exist, but they are so energy-intensive (water has to evaporate) that they're only used in extreme emergencies. Plus, doing it on a large scale would have effects on things we don't fully understand yet (sea levels etc).
Well, no, because the water that comes out of the sea, one way or the other, will probably go back there.
The main problem with desalination is what to do with all the salt it produces. I mean, you can dump it at sea, but then you're poisoning some patch of sea and hoping the salt will disperse.
Also, as another comment already said, you might be able to sell the salt instead.
The most common method of desalination is reverse osmosis. Still energy intensive, but presumably less so than evaporation.