Date & Time issues

I'm having problems with my iPhone 5c and it keeping the correct time. There is nothing wrong with my time zone in the general settings, but once I turn off Set Automatically and turn it back on, it goes back to the correct time. Also my phone has an issue with connecting to my wifi. It tells me on the menu bar, that it is connected but once i go into an app it says i am not. My cellular data is disabled from most of my apps to save my data.