Try going into the Messages settings, signing out of your Apple ID, wait several minutes, then sign back in.
For wi-fi, try forgetting the network, then restarting your router. Yes, I know everything else works, but routers can get hung up on specific devices, and iPad's are notorious for it.
For Google, if you are using Safari, try clearing your data and cookies in Safari's settings. You'll have to log back into everything, but this fixes most problems. On the other hand, several people have been having problems with some of Google's services lately (like Google docs getting stuck in desktop view). I think it's related to the changes they are making to integrate everything into Google Drive.
I'm not going to cover Maps. There are already dozens of threads on the subject.