You can tell by the design of the case. If there are protruding caps with angled corners then its Johnson Controls. If the caps are recessed then I think that's Delphi (or Exide?).
My Nissan is an 07 with 81K miles. Original battery keeps testing out OK. Won't die. It's 9 years old now. Pretty good! When I replace it I will buy one from Costco tho.
Not sure how Nissan works, but the OEM Mazda batteries are Panasonic. We cannot get Panasonic batteries here, the replacement batteries are distributed by Interstate but are made by Johnson Control.
I don't know but I do know when I got my 08 Nissan Altima it already had OEM battery replaced. From what I've read... Those batteries aren't hitting in much at all. I've seen it mentioned frequently in the Nissan Infiniti site.