"How many people are in your family?"
Huh??! How do you know this is the start of a conversation? You and I could be having a conversation for the last 30 minutes and, after getting a little cozy, I could ask you about your family and how many there were.
In such a case, since I don't know you well enough, shouldn't I say "ご家族”？What say you to that？
I also tried ご家族は何人いますか without success. I tried the second time with ご家族は何人いらっしゃいますか and it was marked correct. One explanation I have heard about why the was not accepted is that using ご家族 would imply the use of 敬語. In which case it is more appropriate to go "all the way" and say ご家族は何人いらっしゃいますか。In other words, you shouldn't mix the level of formality in a single sentence.
It's not an ending, it's a quasi-verb in itself like 「です」. The existence of living beings is denoted by 「いる」or in its polite form「います」.「ある」 or「あります」is reserved for indicating the presence of things, it really would be far from correct to use it when asking about someone's family.
Actually, yes. We wouldn't use おります as a question. It is possible to say 何人おられますか though.
A: 田中さんはおられますか。Is Mr. Tanaka here?
B: はい、おります。Yes, he is here.
However, the impression that you give off is probably not very polite.
I use いらっしゃる as it is more polite and is kinder to the listener. Unless it is a friend, then I would use いる.
It would be どの人 (dono hito) from what I've found, but we haven't learned that yet in the lessons.
この人 - this person (kono hito)
その人 - that person close to listener (sono hito)
あの人 - that person over there (ano hito)
どの人 - which person (dono hito)
We did however learn これ, それ, あれ and どれ - the same principle of prefix applies.
from what I have learned いくつ is only used if you use the word つ for counting, if you use other counter words like for example 人 [nin] - counter for people, 個 [ko] - counter for small objects (there are a lot of counter words, but these I learned so far) you use 何人, 何個 and so on.
おります, to not get into too much detail, is kind of another way to say います. Specifically it's humble language that you use in highly formal situations when referring to yourself/your own "circle." That said, it wouldn't really be appropriate in this context, where you're directly asking another person about their family, so I suspect it's an error on Duo's end and they meant います (as in the displayed answer on this page).
Why is は used? Why isn't it に or even には? Would that have some implications of people living inside the bodies of the family members or something? And so, wouldn't the sentence be more accurately translated something like "Of how many people does your family consist?(a bit awkward, yes, but it makes more sense in my non-native English speaker mind this way)"