You probably need to read this and understand how unintoduced things are presented to the listener using det: https://www.duolingo.com/comment/9708920
In this exercise, they is the plural of it. It is not the plural of he/she, like in your examples. When in the presenting case, det can be singular or plural and can be either gender.
"That are my scarves" is definitely wrong.
"They" is always correct in this case, and "those" could be correct depending on context. "Those" is used to contrast the items in question: e.g. "Do you see the scarves with the stripes on the ends? Those are my scarves."
Yes. In the case where you could be pointing to something, "that" is usually translated to den där or det där. In the more metaphorical case, yes, "that" can translate to det. Take for instance Att vara eller icke vara. Det är frågan., the Swedish translation of the famous Shakespearean quote. (icke is an archaic form of inte.)
dem is wrong, because that's the third person plural objective case, or "them" in English. ("Them are my scarves" is spoken in some dialects, but would be considered incorrect by most.)
de as a definitive article would be wrong: "The are my scarves". de (spoken as dom) as the third person plural subject should be accepted.
Unlike English "it", det is used for both singular and plural, when det refers to abstract things. An abstract thing could be in the sense of det regnar ("it is raining") or when the actual item or items haven't been introduced yet. In this case that abstract things would be mina halsdukar. I think the point of this sentence is to demonstrate this usage.
I would appreciate feedback from a native speaker :)
I disagree, De är mina halsdukar sounds wrong. Possibly if you point right at them and stress de very strongly. This is still the presenting construction where we use det when we start talking about something, regardless of gender and number of the thing. Just like we say Det är min bok, not Den är min bok.
I wrote a much longer post about this here: https://www.duolingo.com/comment/9708920
Wait but we've learned De is they - and I've also read on a few occasions that when Det is said the T is often silent, so I'm sure when spoken there isn't a huge difference between the två,
But officially, why isn't it De är? Is De only used when referencing people and not objects?
Only det is used to introduce a topic like here. It doesn't matter if the thing is neuter, common gender, or plural, we always start out with det.
det är min hund 'it/that is my dog'
det är mitt hus 'it/that is my house'
det är mina böcker 'they/those are my books'
det does not refer to the dog, house, books or whatever, it's just used to start the sentence.
Much longer explanation here: https://www.duolingo.com/comment/9708920
Multiple versions of this exercise lead to the same comments. I think the version you are talking about expects you to know that "mina" can only be used with plural "halsdukar", not with singular "halsduk", so there is only one correct answer to the multiple choice question.
I was also contemplating this, because of another exercise. I was trying to figure out if "Det där är" could be those are and "Det är" could be they're.
They can be an anaphor: https://en.wikipedia.org/wiki/Anaphora_(linguistics) eg "Do a tree's leaves turn brown before falling? Yes, they do." It would sound weird to reply "Yes, these do" or "Yes, those do" unless adding some gestures or emphasis to compensate. Leaving it uncoupled from a concept of proximity, it works as they. It's the same with a more definite object like "My eyes hurt; they do that sometimes". Another sentence: "Leaves fall, after they wither." could optionally begin with those leaves or these leaves, but not with anaphoric they.
Since you taught me that the "Det är construction" is used for something that is not yet introduced, I decided it might not be able to translate to they in those cases. Det ar seems the opposite of anaphoric.
Just my thoughts. I began by questioning whether I even knew the difference in my native English and I'm still not convinced I know what I'm talking about ;)
Thanks for your input! I need to think some more about this general subject, I should probably dig up my old Silver Bible (big English grammar book) too and see if they have anything to say about it. I'm planning to write a more general topic about this and that to try to sort it out a little more for students. For instance when you say things like 'I told him that' or 'I know that', it's possible to say det där in Swedish, but we'd be much more likely to say det instead in most contexts.
They can be interchangeable. I would use those when pointing to something, or when referring to an object in the same or previous sentence, e.g. "The scarves on the table? Yeah, those are mine." In any other case, and always when referring to people, I would use they.