"There is one person in the room."
人 (hito) is the noun meaning people. 一人 (hitori) is the counter. Counters do not usually take particles, so your suggestion wouldn't work. I think 部屋に一人います (heya ni hitori imasu) should be correct, but it was marked wrong for me today.
As for why there would be 人 twice in the sentence, I think it's easier to understand if we use a counter that has a different kanji from its noun.
Banana ga nihon arimasu.
There are two bananas.
This is the structure that this sentence is using.
@IsolaCiao 1st. Thanks for 方 explanation below (from italki).
2nd. Other comments claim single readings intentionally differ to teach Japanese learners to recreate natural Japanese instincts when approaching their native written language.
Many films integrate short exchanges concerning readings and characters -- sometimes to clear up misunderstandings, sometimes as comedy.
Other comments claim these 'alleged mistakes' are intentional and helpful.
I'm glad those users find them helpful, but they're definitely mistakes.
It seems the post I linked to has been deleted without explanation, but the contributors have expressed in other threads that they can't control the TTS such as here:
Unfortunately, Duolingo's system isn't always ideal for a language in which the same word/character can be read more than one way. Since the audio is TTS (text to speech) provided by a third-party provider, we (the contribs) have no control over which reading the TTS chooses, and when a word/character is provided as an individual tile, it's read the same way throughout the entire course, even if that reading isn't correct for the context of a particular sentence.
I'm hopeful that there will be some point in the future in which we have more control over the TTS audio and can correct errors like this, but at the current moment, it's a technical limitation of the system.
This maybe is not a good translation, because the subject/topic is different and it actually answers a different question.
Question 1: Is there anyone in the room with that person? その方と一緒に部屋に誰かいますか？[人 or 方 would be correct here?]
Answer 1 : "(No,) The person in the room is alone" 部屋にいる人は一人です。[部屋にいる方は一人です。方 is ok here?]
Subject= [The person in the roomは] is alone. Similarly, [xは] is a lawyer. 部屋にいる方は弁護士です。 or 部屋の中の方は弁護士です。
BUT, Question 2 : How many people are in the room? 部屋には何人いますか？
Answer 2: 部屋に人が一人います。 There is 1 person in the room.
The same structure allows for counting a varying number of people.
[any help with my explanation would be appreciated]
that is because the language tree of the Japanese and English are so far apart... so naturally, the grammar would be nonsense to English speakers.
as for English, German, French, and Persian (my primary language) they are so similar in general and different in details. fortunately structurally Persian is so similar to English and has high flexibility like Japanese so I am having an easier time than you guys although there are some cases that are exceptions.
so I think for learning other languages it is crucial to put yourself in their position and see how they approach and interact with the sentence. Although it is important to grasp the meaning by translation, it is not the main goal (for me at least). have fun. :-)
I'm not sure you'd hear 方 very often.
You might have a person serving customers who would use お客様（おきゃくさま）and the counter 名様（めいさま）[technically the counter is 名). So you often hear お客様何名様でしょうか？（おきゃくさまなんめいさまでしょうか？） How many people? [for a reservation, table, etc.]
But you'd usually answer with 一人、二人, etc. You could answer with 一名、二名, etc., as well, though it seems to be less common. It's not really considered much more polite, either, though 名 is used in more official circumstances, from what I've heard.
方 can't be used by itself like that.
Note that there is one case you cannot use "kata" instead of "hito." "Kata" should be always modified some other preceding word/phrase/clause. It can't stand alone.
For example, 部屋に人がいます。 There is a person in the room.
This "hito" is not modified by any word. Therefore, 部屋にかたがいますis wrong.
If you change the sentence like this; あの部屋にいる人はメリーさんです。 The person who is in the room is Mary.
This "hito" is modified by あの部屋にいる, so あの部屋にいらっしゃるかたはメリーさんです。is correct. (The verb いる becomes いらっしゃる in honorific speech.)
I know it should be the same meaning but in Japanese, unless you already know we are talking about a person you say ひとりの人. This is because hitori's 人 represents nothing. In Japanese, when we count a number of persons, things, animals etc, we sometimes put counting noun before the noun. I.e. いぬ、dog accompanies with ひき or ぴき(匹) and 'Two dogs are there' is にひきのいぬがいます。because we cannot say に いぬ がいます。 Japanese has many counting nouns but excexpt for the counting noun for person ひと、you learn whenever you think it is necessary.
It should be ひとり, see above: https://forum.duolingo.com/comment/24184336?comment_id=36549217
No, 一人 is a counter so we wouldn't put が after it.