You are going to need to replace the volume/headphone flex assembly inside of the phone. If you have not worked inside of an iPhone before I would recommend taking it to a local repair shop to get diagnosed to make sure to find the exact problem. You might be lucky and it could be a loose connection.
I would try and replace the battery, but this is most likely a logic board issue because of the age of this device. In my honest opinion I would upgrade.
Best software for doing what you are stating is CopyTrans Manager (Click the words for the link to the official download page.) Directions are pretty straightforward and it much more simplistic than iTunes.
Place the grounding clip on top of the screw hole marked by the orange circle with the gold tab (shown by the red arrow) pointing down. Then attach the battery to the terminal and screw in the two screws as shown by the circles.
Most likely this was caused by a non-genuine Apple accessory, e.g. the cable or wall adapter. I have never seen sparks come from the outside of the phone, only time it has happened to me is inside of the iphone touch contacts near the battery. When it starts to get hot that is usually a sign of a short caused by water damage or a severe fall.
Yes they are sold at many places online. They range from $80-$150. Here's a trusted dealer to go through: http://www.etradesupply.com/apple/ipad/a...-ipad-4.html?limit=all Or use these guys to do it for you: http://www.iresq.com/ipad-repair/ipad-1g/ipad-back-case-repair-service.html http://www.ubreakifix.com/ipad-1-back-housing-repair/
I would recommend to either get a case that would not allow it to move. Like Dustin said you cannot just buy the glass and replace it that way. It requires very expensive equipment to do that. I would also look up your serial on Apple's website and see if it's under warranty. If it is, then schedule a Genuis Bar appointment at the nearest Apple store to see if they would swap out the part or phone for you. https://selfsolve.apple.com/agreementWar...