1) It is the Genuine and Authentic Pentax battery which was shipped with the Pentax S4i.
2) I would always suggest purchasing the genuine branded Pentax battery so you know what you are getting. You just don't want to mess with possible mismatches or where a generic is made to fit multiple applications.
3) If purchasing online from others...make sure you get the true thing. Know what you are buying.
4) Yes....the picture on Amazon is not accurate. It is not black...rather grey. I can assure you I received the genuine battery.