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You might want to try a software repair via sony update service,but you could have a defective unit.So the best thing is to take it back.
The phone.Do try a repair,maybe it helps.
Not sure you are talking about what I have (and heard someone else at least have the same):
When plugged in (haven't checked usb-to-PC, only AC), while holding touch, the dragged thing vibrates on the screen. No issues unplugged.
The tearing. Do you mean reverse landscape? (Phone turned 90° to the right (clockwise)) That one is solved for me since 1.14 update.