"She has some relation with that group."
Translation:Lei ha qualche rapporto con quel gruppo.
According to Maiden and Robustelli, the singular alcun and alcuno are unheard of outside negative expressions and rare in those (meaning the same as nessun/nessuno). This sentence requires a singular.
In the plural, alcuni/e means a few, while plural qualche (invariant) roughly means "the odd" as in "These are all supposed to be screws, but check anyway; I'm always finding the odd nail."
"A Reference Grammar of Modern Italian" (Maiden and Robusttelli, 2000, p. 152)
The meaning of this English sentence is itself unclear. "She has some relationship with that group" would be better. As for the "rules" of Italian grammar outlined below, I suspect that most native Italian speakers a. don't know them, b. have better things to do than learn them. Meanwhile the cues and "correct" answers on Duolingo Italian are often faulty, but "reports" get no response; in contrast to Duolingo German. Why is that?
Quello can be an adjective, but it changes form depending on the word that follows. Only if the word is masculine, singular, and uses "lo" as its article can you use quello. So you have:
quelo zaino that backpack quel ragazzo that boy quell'albergo that hotel quella giornata that day quell'università that university quegli zaini those backpacks quelli ragazzi those boys quelle giornate those days quelle università those universities
"Prego! An introduction to Italian: Fifth Edition" (Graziana Lazzarino, 2000, p. 81)
Since "giusto" does not begin with z or s+consonant (that is, you say "il giusto" not "lo giusto") it would take quel, not quello.
Strictly speaking, in the sentence "L'ingrediente nella scatola è quello giusto" I think "giusto" is an adverb because the sentence means "The ingredient in the box is that one exactly." Although I suppose it could, as an adjective, equally mean "The ingredient in the box is that exact one."
If "giusto" were a noun, then the thing in the box would either be a person or a right, and neither is an ingredient. Giusto as a noun does not mean "just"; "just" isn't a noun in English either.
So by any analysis, "giusto" cannot be a noun in the sentence and therefore quello must be a pronoun.
In this case "giusto" is an adjective, not an adverb.
"quello/quella" are pronouns they doesn't modify for the word that comes after them, it means "the one" or "that one": "lui è quello giusto" "lui è quello sbagliato" = "He is right one" "He is the wrong one". It can be alone: "Quale? - quello!" = "Which one? - that one!"
"quel/quello/quell'/quella" are adjectives: "quello" (plural "quegli") stands before "z", "s+consonant", "pn", "ps", "gn", "x", "y" and some rare exeption (particular "il dio" that have plural "gli dei"), "Quell'" (plural quegli) stand before vowel, "quel" (plural "quei") in all other masculine cases. It means "that": "Quel giornale è di ieri" "That newspaper is yesterday's" it needs some noun after, can't be alone.
So when "quello/quella" means "the one/that one" it is a pronoun and doesn't inflect, when it is like the adjective "that" it inflects in "quel/quell'" and is before a noun.
I agree with what you say, the thing that convinces me is where you say " .. I think "giusto" is an adverb because the sentence means "The ingredient in the box is that one exactly." This is also my understanding of the use of quello as a pronoun, and in that case it would not change according to gender. Thanks for clearing that up.