Can I go to Hainan island and be back to China?

Your single entry visa for China is good for travel throughout the country, including Hainan province (island). So, if you enter China on your visa, you can travel to Hainan in the same way as you are traveling between Beijing and Shanghai and you don't need any kind of visa or any kind of an announcement. This is normal domestic travel and after Hainan you can normally return to the mainland part using any mean of transport you wish. To conclude, by traveling from mainland China to Hainan, your visa will not be consumed. It will remain valid until you exit the country or when it expires because it has some expiry date. You are free to visit Hainan on a single entry visa several times in a row if you wish.