IPhone 5S Covered in Apple Warranty?

I have an iPhone 5s and overtime I have used it without a case, the sides and particularly the top of the housing has been roughly kept with dents and a number of scratches. The back of the phone has a thin scratch which isn't noticible, but the main problem is the switch and sleep wake button keep sticking forcing me to use the accessibility settings to operate them. This is very annoying, would apple replace this as I'm still in my one year warranty and haven't actually used it once yet. I'm asking here first as the nearest apple store is around two hours away! This is all mainly due to the kids using my phone and a very busy work! Much Appreciated (images attached) - JoshIPhone 5S Covered in Apple Warranty

Realistically? You can try, but don't hold your breath.
Your mention of "roughly kept" and "due to the kids" sums the situation up fairly accurately.
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However, its Apple's decision to make.
Being blunt, I 'suspect' you'll be advised politely… No way Jose!

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