Either the left headphone is shot or the headphone jack is messed up. Try a different set of head phones if its same result see about replacing the jack.
The battery does not hold charge. It is weak. Replace it with same type number. Brand name of the battery isn't a matter, check its type number printed on it.
http://electronicshelponline.blogspot.com/
Hi Brian,
It would seem obvious to contact Sony customer support. Failing that, you need to have access to another phone (in English) and use that as a "template" to work through the settings menu.
Probably suffered damp ingress while in storage, and thus some conductive internal corrosion; use a test meter to see if there's any leakage when it's switched off and take it from there...
Either that or use AA Nimh rechargeable batteries