"Are there two?"
I'm not sure what the app tips look like but the web tips show the pronunciation written in hiragana alongside the kanji form.
Number Form of つ Form of 個 １・一・いち 一つ・ひとつ 一個・いっこ ２・二・に 二つ・ふたつ 二個・にこ ３・三・さん 三つ・みっつ 三個・さんこ
It is pronounced ふたつ because ふ is the original Japanese reading (kun'yomi) for 二 and using ~つ is the traditional Japanese way to count various things.
に has become more common over time but it's the originally Chinese way of saying 2 (on'yomi) and ancient Japanese used to count ひーふーみー, not いち、に、さん. Sometimes you can still hear it if you're lucky.
I'm on the app, so I can't tell how old this comment is but here goes:
つ is the most general counter. 個 on the other hand, while having a wide range of uses, isn't quite as general as つ. In this course Duo seems to want us to use 個 for counting small, round things (which is a common use for it), and use つ for stuff in general.
Since we don't have any context for what we're counting in this sentence, Duo wants us to use つ.
Right now, we're just beginning to learn how to count (small) things in Japanese. Depending on where you're from, this is probably going to be one of the more difficult aspects of learning Japanese.
I'm lucky in that I have a couple of books that thoroughly describe the way that things are counted. Many, if not most of you don't have such luxuries. However, I've found a site that covers this all pretty scrupulously.
I hope this helps.
Unlike English, there are absolutely no obligation in Japanese to place a subject or an object in any sentence if the context is clear. Technically only a verb is required, but that can also be omitted in some cases.
- よろしく (only an adverb)
- よい旅（たび）を (only an adverb and an object)
- 気（き）をつけて (an object and a verb in an incomplete clause)
On your point "Japanese counters change depending on the subject," in this sentence 二つ is the invariant form (does not change with the subject). English counters also change with the subject,
- two pieces of cake 二切れ（ふたきれ）のケーキ
- three pairs of glasses 三本（さんぼん）のメガネ
- one teaspoon of sugar 小さじ一杯（こさじいっぱい）の砂糖（さとう）
True, Japanese does like to omit the subject of the sentence. But if you have context, the meaning of a single sentence can change. Simple sentences in the start of learning are all good, but when reviewing it gets a little harder when you know that context is very important. If there is no context it is difficult to accurately translate from language to language. Without it, simple Japanese sentences that only have the verb have little meaning. Assuming the meaning gets us no where as linguists
English does have it's counters, but you can (in some cases) not have the counter as they are implied. Not exactly true with Japanese. As I am currently living here, several of my Japanese friends have corrected me and encouraged me to use the various, if not unending, different counters for the specific objects. So merely stating 二つ when talking about an animal even if it is understood, is strange
Yes, I agree with what you have said - in duolingo it is difficult to imply context, and to avoid generic counters when specific counters are more appropriate.
However, it does not answer the grammatical question "Is it correct to say 二つがありますか ?" - the answer is that it is technically correct, but the meaning is different. I am going into some details.
When a counter acts as a subject (or object), this counter is a specific group where by context it is known to the participants of the conversation. It is very unnatural to use 二つ in this case but I managed to make up one. Please look at the following example:
- ジョンとマリアは私のクラスメイトです。二人があそこにいます。 John and Maria are my classmates. The two are over there.
- A: 部屋に田中さんへのプレゼントが３つあります。そのうち、一つが左の袋にあります。B: では、右の袋にのこりの２つがありますか。 A: There are three presents for Mr Tanaka in the room. Of the three, one is in the left bag. B: Then, in the right bag, are there the remaining two?
When the question says "Are there two?" it implies that the "two" things are unspecified. Otherwise it is better o specify "the two" or "two of them" explicitly to indicate the things are specific and known. When the things are unspecified, the counter cannot act as a noun. It can only act as an adverb, so ２つあります rather than ２つがあります.