Power Saving is not Power Saving. It kills the Note 1 in less than a day. Not sure if they fixed it on the 3 but I hid the icon so it won't be activated accidentally. Remove your battery and put it in again after 15-30 mins to reset the phone. And don't use Power Saving ever again.

Never used antivirus on the phone. It's connected to the Net most of the time and so far nothing strange has happened.

How bright is your screen? Setting it to Auto might help.