“Octopi” is only “correct” because of common usage. Octopus does not have a Latin origin, so it doesn’t make sense to pluralize it that way. Which is to say it’s not technically correct, it’s just “correct”.
In the proper format of this meme, the wojack in the middle should be obsessed with technical correctness, while the one on the right is fine with merely “correctness” (as in, enough people use it to make it understood).
But since you can understand it, the format is merely “correct” (I’m being tongue-in-cheek to make a point)
Octopuses is correct if you’re referring to many different species of octopus. Octopi would be correct if you’re referring to a cluster of one species of octopus.
Great question. When I hear people I think that’s used to draw attention to common relevant traits “people of England” for example. Persons is more a group of less related individuals or at least with less relevant similarities “persons of interest” for example
I mostly write 'indexes' these days when I'm not on autopilot, in part since not all of my coworkers have a high English proficiency and just following the normal +(e)s plural makes it easier. My brain really does not want me to write 'matrixes' however (and indeed, my dictionary in this browser is fine with 'indexes' but not 'matrixes'). I also try not to be pedantic with verbs whose irregular forms have become less common than their "incorrect" (at least when I was taught) forms. "Shined" being one of these, but I am sure there are more.