No to wearing it while taking or shower, or swimming. However, it gives you time to charge it a little, and gives your wrist a rest.
Yes you can wash your hands while wearing it, unless you are completely reckless and put the watch directly under the water. I wash my hands all day long, but I'm always careful to not get too much water on it. It is water resistant, but you don't want it submerged or hit with heavy streams of water.