Iphone 5s is having problems with update?

I tried updating my iphone 5s everything was going smoothly till my phone kept turning off and when I would turn it on again the little usb cable with the itunes sign was there and I had to keep trying to update it over and over again and my phone just won't stay on and the battery percentage is at 80 so its not a battery problem. Not sure what is wrong but its frustrating because now I can't use my iPhone since all that is on the screen is USB cable. What do you guys recommend?

Added (1). also the cable is fine its brand new but the iPhone won't stay on it keeps turning off and I turn it back on trying to use recovery mode but it only stays on for a few seconds and the usb cable is all that appears

IPhone won't charge while in use?

So I recently bought an iPhone 6 and before this I had an iPhone 5c. I've noticed that if my iPhone is plugged into the charger it won't charge if I'm using it. Its not a huge issue for me but I thought it was strange because that has never happened with my old iPhone or any phone I've ever had before. So is there a way to fix that?

16gb iPhone 6? Is that enough?

I can't spend the money to get the 64gb right now. I have an ipod for music and if I want' to watch videos I'd just use youtube. I don't use apps much, just Skype, a game or too. I do like taking pictures and videos but I don't do it so often.

My iPhone 5c won't connect to Wi-Fi? - 1

I moved a few weeks ago and just got Wi-Fi today. Everything works great on my iPod and computer just not my phone. I reset the settings, restarted my phone and I know I'm using the correct password from what I know. Any tips?