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Check if there's any dust or something inside the headphone port, you can clear smartconnect app data
That seems like a hardware issue but boot on safe mode and report back
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
Keep us updated.
Repair the phone with PCC, if that doesn't work, contact your local Xperia Care http://support.sonymobile.com/global-en/contactUs/
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
it will be the latest update available to your phone, if you have the lollipop update notification then it will update your phone to lollipop.