iPhone 5 only charges while turned off

I got my phone and it had about 80% charge. I let it drain first use and I plugged it in to the wall charger after. It only charged up to 57% and it stopped charging. Whatever I did, the phone wouldn't charge. After a few hours, the phone died and I tried charging it again and the charging symbol showed up. It charged enough to turn the phone on but then it wouldn't charge anymore.

Is it a bad lightning cable or the phone itself?

Another question I have is that the phone doesn't seem sturdy on the top. When I tap the top part of the phone near the camera lens it sounds like it wasn't manufactured well. Is the phone like this or did I get a faulty phone?