My iPhone won't connect to the App store + iTunes? (urgent)?

I have to download the app for school on my iPhone 5c, but its not connecting to the app store? I changed the time to automatic, and I did everything but my iPhone is not working. Also, my time displayed on my phone is always messed up, and my Wi-Fi cuts out almost ever minute. I logged out of my apple ID, and tried logging in again but it won't let me log in again, and it says "Can't connect to iTunes" please help?

Try to use your cellular data to download. Your internet may be screwed up. Also, try holding the power button and home button at the same time for a cuple seconds until you see the Apple logo. This restarts your iPhone and will sometimes fix problems like you are having. I do this all the time!

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