What will APPLE do to my iPhone 5?

Ok, so I bought an iPhone 5 16gb used.
I checked if it had warranty, and it does have warranty.
I notice that my battery doesn't last long and drains little by little even when not in use. I disabled every cool features from ios 7, but I can't seem to get good battery life on my iPhone 5.

1. If I take it to apple, what do I need, to prove them the iPhone has warranty? And what will they ask for? Receipt?

2. Will Apple replace my battery the same day? Or it takes days?

3. What will Apple do to my iPhone?

Yeah theyll ask for proof of purchase only the orginal buy can use the warranty

If its used then its hard to tell if the previous owner took care of it.

The Warranty is most probably on the serial number, not a receipt, and the battery if you decide to do it your self, won't take more than 15 mins to install, and i don't think that they well do it in the same day, and if the problem happened with iOS 7, then just downgrade to iOS 6 till the problem gets solved

Apple can tell warranty by the serual number and they will want you to restore as a new device before repairing or replacing it to see if that corrects the issue.

If apple refused the warranty repair then you could do it yourself. It's very easy. Go to youtube and search for "how to replace battery for iphone 5". The battery cost around $10 to $20 on amazon or ebay.