Regarding the battery, it was not in the original packaging but it was still well protected.
Despite the concern not to see that the battery load the first few minutes of charging, the smartphone is switched on after five minutes of charging. I guess the battery was completely empty, but now everything works perfectly.
Finally, after a few weeks of use, my Samsung Galaxy S3 Mini holds much better than before the load. I can keep it lit smartphone for 2 days (against less than a day with my old battery).