"These are not his cookies!"
Translation:To nie są jego ciasteczka!
"To jest/są X" and it's negative "To nie jest/są X" are constructions that take the Nominative for X.
Here we just have the nominative plural for cookies = ciasteczka
the jego bit is easy, jego doesn't have to match gender case or number when it means "his" (it has other meanings too, but here it means just "his").
Here, "these" is not a determiner, but a dummy pronoun, serving as the subject of the sentence. In Polish it will always be "To", used for "This/That/It is" and "These/Those are".
"te" would work in "These cookies are tasty" = "Te ciasteczka są smaczne", where "these" is a determiner.
CI mężczyźni - for masculine human (i don't remember the exact name) plurals
te kobiety, ciasteczka - everything else plural.
In this context 'to' means 'something' and you don't worry about gender and singular/plural. 'to nie jest jego brat/siostra/dziecko. To nie są jego bracia/siostry/dzieci. BUT:
Te ciasteczka nie są jego. Ci mężczyźni nie są jego braćmi.
Genitive is required for negation, only when the positive sentence had Accusative. Accusative is probably the most widely used case, so learners just get used to 'every negation = Genitive', but that is not true. The other cases do not change when negated. Negated Instrumental is still Instrumental, negated Genitive is... well, Genitive, etc.
The sentence here is basically just a simple "This is X" (or rather "These are X") sentence, so it uses Nominative and stays in Nominative when negated.
You're quite close.
If your sentence was "Te ciasteczka nie są jego", then it would mean "These cookies are not his".
Your answer also makes some sense, but it's rather unlikely: "It's the cookies that are not his/that do not belong to him" (You claimed that the thing that doesn't belong to him was the rubber duck, but actually the thing that doesn't belong to him are the cookies). This meaning, which I can only explain by giving such examples, is one of the many meanings of "to".
Well, let's start with the fact that this is not the Accusative pronoun. This is simply the possessive "his" and it is always "jego", in every case (yay, something doesn't change in Polish! also "jej" = "her" and "ich" = "their" don't change).
But answering the question anyway, "go" is the basic, neutral form, while "jego" is emphatic. So for example "Lubię go" = "I like him", but "Lubię jego, a nie ciebie!" = "I like him, not you!".
I still don't quite get it. You say that "his" is always "jego," but "go" is the genitive form of "on." So, because of the "są," the object is in the nominative case. Should its possessive pronoun be in the genitive, as I thought? Genitive is used to show possession, right? Is the need for stress (emphasis) the only reason "jego" is correct? Or is "jego" the only possibility in a sentence like "Jego pies pije wodę?" Not "go pies?"