There are showers and per the Disney web site (a good resource for this information), there are some dispensers for shampoo, though they recommend you bring your own. I can see them being empty rather quickly and it could be some time before a CM can refill them.
Yes, there are showers and changing areas. Yes, there is (cheap) shampoo.
What are they like? About as nice as public showers that get well used can be. A bit icky, but passable. The showers, and water park restrooms in general, tend to be in a constant state of being "wet" everywhere - just a very damp/humid environment that isn't somewhere you really want to spend much time. Water park shoes or some type of shoe you don't mind getting wet can be helpful.