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Have you read this topic about your battery and charging issue? It could be useful:
/t5/Xperia-Z2/Lollipop-charging-bug/td-p/965384
Keep it friendly, if the suggestions presented to you aren't working then contact your local Xperia Care
Click on @alexdon 's link or just re-install lollipop but make sure its a clean install, which means, delete all the apps.