Translation:Will you use a chair?
True. The te-form would make it clearer that it is progressive or -ing form in English, but the problem is that masu can be translated into progressive tense too. Since there's not context, it can be taking as either: Are you using the chair? (which generally sounds more naturally/instinctive for an English speaker) or Do you use chairs? As Goren points out the latter makes more sense from the Japanese speaker’s perspective.
I think the -masu form (when talking in present) being translated into progressive tense just comes from the fact that many things happening in the present can interchangeably be expressed in present simple or present progressive/continuous, also in English. But I would try to keep them as they were in Japanese, at least in Duolingo. There's also an additional complication: in English, progressive form can also be used to indicate future (which is represented with the -masu form in Japanese). Being especially aware of that will probably be useful when trying to translate into "what feels natural" in English
True, you get this issue in French as well. Just b/c French has a progressive tense reserved for now (...en train de...) doesn't mean it is used for the 'now' action. (I am sleeping now = Je dors maintenant) Even English, which tends to more strictly reserve present simple for habits, routines or general states, often strays in colloquial oral English (Eg I'm working on Fridays, I'm working way too hard each day)
That kanji "椅" was of a classification that could not be used for official documents until quite recently. (It was added to the common-usual kanji (常用漢字) defined by the government in 2010)
Many of us still write in hiragana "いす", or katakana "イス". (especially in hand writing)
"Are you going to use a chair?" sounds more natural, but "Will you use a chair?" is grammatically correct. I think your sentence comes across sort of stiff and implies something that will happen in the future. It would feel more appropriate to ask "Will you use a chair" if you were having a discussion with your friend about how he is going to try to take something down for a top shelf later on, rather than in the moment.
つかう means "to use", so the sentence means "do/will <someone> use a/the chair?> "will you use a chair?" would be valid for example at an event where there is a pile of chairs that people can use to sit, and you're going to get one, so you ask your friends if they're going to use one
I read this entire section and I'm still a bit confused. In English, we don't really use "use" in this way (at least, where I'm from.) If we're asking if someone wants to "use a chair" we're more likely to ask "Will you sit on a chair?" That's not what the words in the Japanese sentence translate as, though, so I think a better question to ask is the following: How is "tsukai" usually used in Japanese everyday speech? I know it means "use" but is that in place of other verbs such as "ride" "sit" or whatever else? For example, could I say "I use the cat" instead of "I pet the cat?" Or, "I use the tree" instead of "I sit in the tree's shade?" How far does "tsukai" go? And is how a thing is being "used" implied, like the subjects of Japanese sentences?
And in such sentences, were is the emphasis? On the object or the action? If, using this sentence as an example, the intent is to ask someone if he or she sits on chairs as opposed to sitting on the ground, the emphasis should be on "chairs." Perhaps because the wording is so strange in English, my mind puts the emphasis on the action, "use." So the question in this case would be wondering if the person does anything at all with chairs, as opposed to asking about what the person's preferred sitting device is.
I'd legitimately like to know the mindset behind this sentence construction.
Saying 座ってみませんか (suwatte mimasen ka) sounds like you are in a store and the clerk is asking if you'd like to try out a new kind of chair. If you wanted to offer someone a seat, I think よかったら、どうぞ (yokattara douzo) is pretty standard. This Japanese sentence isn't trying to offer someone a seat, though, it's just asking if you will use a chair (maybe you're sitting on the floor, maybe you are trying to reach something high up and standing on a chair would get you there).