Q: iPhone 6 issues iOS 8.3

Since yesterday my iPhone 6 (ios 8.3, got a new battery) does very strange things:

It randomly shuts itself off when I still have 90% left! I restart the phone and it changes the time to january 1 1:01. When i turn on my WiFi, the time changes back to what it was before. This process happens like every 10min. The phone also doesn't show my carrier at the top and it says 'searching' but I can still receive and send messages. My dad and my aunt have exactly the same problem... I think it's a bug in the software or a virus. Someone having the same problem? Can I solve it? (downgrading to ios 8.2, resetting)

Greets,

Lewis