Translation:How many chairs are there in the room?
Does this mean both "in a room" and "in the room"? (I had to translate the sentence and I only had indefinite particle "a" which sounds a bit unnatural to me unless you're asking "How many chairs are there in every room?" which I think would have a different translation in japanese.)
Would people type this out with the full Kanji, like "部屋に椅子は幾つありますか？"
I'm finding it burdensome the way I am being introduced to a lot of new words but not introduced to the Kanji; this is going to create extra work for me later on to learn these Kanji on my own. If they're Kanji that are rarely used, it's not a big deal to me, but if they're relatively commonly used, i.e. I'm likely to encounter them in daily life, it is important to me.
I don't need the Kanji to be thoroughly introduced through matching exercises...they can just teach them when they teach a new word.
I would love to have a toggle that turns on full Kanji.
I can surely tell you, the common representation is 部屋にイスはいくつありますか。椅子 and 幾つ are not commonly used and いす is commonly written in katakana.
I agree that kanji should not be introduced in an early stage. What Duo can do better is to include spaces between phrases to increase readability, like this
へやに いすは いくつ ありますか
We use に instead of で when talking about the location where an object exist (after the action has been taken if any).
For ある and いる (existance for inanimate or animate respectively) we always use に to indicate the location. If you use で, it would make the preceding noun as "the terminal state of the subject." (である=です in normal form)
As far as I'm aware, Duo ignores punctuation (aside from apostrophes) so the only way to show that you understand it's a question is through word order.
Also, this is a more advanced consideration, but "there are how many chairs in the room?" reads more like an exclamation of disbelief, rather than the genuine interrogative of the Japanese sentence here. There are other constructions in Japanese which would better convey the disbelief of your suggestion.
There are two buckets of kanji: common and uncommon, as published by the Government's literature and science department (文部科学省). 幾（いく） is an uncommon one. Even some native Japanese cannot recognize this kanji. It is common practice to write only the common ones in most of the day-to-day usages. In literatures you may find uncommon kanji though.
The full common kanji list is published here: http://www.bunka.go.jp/kokugo_nihongo/sisaku/joho/joho/kijun/naikaku/pdf/joyokanjihyo_20101130.pdf
Yes, but also as I've already answered this question on this page:
「From a translation perspective, I would say it's fine. But for a learning exercise, "inside the room" should be へやの中」
So the course developers may not ever get around to changing it, if they share my opinion.