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To diagnose the first, we'll need more info. What is the phone, how old is it, how old is the battery, at what level of remaining charge do you normally recharge, what do you use the phone for, what is your screen brightness level, what are your signal strengths like?
To fix the latter, go to Settings, Display, Home Screen, Wallpaper, and then the same, except Lock Screen, Wallpaper. The two are separately settable.
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