My iphone 5 had have scratches as ibought it.. But at the repair center says that this kind of things are not covered by guarantie.. Wtf???

You won't feel too happy about this but there is very little you can do unless you bought the phone from an Apple retail outlet and are looking for replacement in the country that you bought it. Then you have a short period when you can return the item.

The first rule of buying anything is to examine the purchase as soon as possible, preferably in the store, and report anything wrong. Once you take it away, the seller can claim you caused the damage. The warranty does not cover damage of the kind you describe.

You will have to check your warranty about the battery; I do not have an iPhone but the link below explains about warranties and batteries.

Apple - Batteries - Battery Replacement

Hope this helps.