probably a broken headphone port, you tried plugging some headphones in and then unplugging them see if that helps? also maybe its a software issue of some sort you could try a factory reset if youve restarted the phone already and that didnt help. my main advice though is plug in some headphones, then yank the plug back out, see if it fixes it, if not who knows. also if youve been messing with stuff like installing custom roms that might have something to do with it too

 

you cant... you can however back them up using titanium backup or something then try restoring them later, or even run cwm then make a backup just in case it doesnt work so you dont end up having to go through the process of backing up the individual apps then restoring them you can just restore everything as a whole. my guess is that wont fix anything but its worth a try before having to ship it off to zte and then wait for a new one

 

Im not saying diy its not hard...had a palm do it 10 x its caused by moisture in the hdphn jack or pushing the jack in too hard like cords to short and u put the phone in your pocket without wrapping it around the phone once ....something i learned to do....the first time i went by a sprint store and they had a phone mechanic guy take my phone apart and replace it... my phone wouldnt play music no game sounds but it would ring if a call came in lol