Hmm. I translated this (without really thinking) as 'don't sit IN this chair', and I think that should be accepted. I would typically say 'sit on' for an armless chair, and 'sit in' for one with arms, and I haven't yet seen anything to lead me to believe there's a distinction in Russian.
An armchair of the kind I would be inclined to say "sit in" is called "кресло".
I wouldn't be 100% certain on that one, but I do find similar results searching for деревянное кресло.
Edit: native speakers divided, so your variant is probably OK. Three votes for стул to two for кресло, plus one for "какой-то креслотабуреткостул-мутант", which probably counts as spoiling the ballot.
Russian uses «тот» much less often that English uses "that". When there’s no contrast between «этот» and «тот», «тот» is quite rare. So English "that" often gets translated with «э́тот».
садиться always triggers accusitive?
It seems like Russian would distinguish between "I was sitting on the chair" (I would guess imperfective verb, prepositional chair)
versus "I sat on the chair" (I would guess perfective verb, accusitive chair)
Right, сади́ться is always used for the action of descending to the chair. For 'being on the chair', you use a different verb, сиде́ть. 'I sat on the chair' is «Я сиде́л(а) на сту́ле».
стул и стол always get me, I think they ought to be less harsh in counting it as a major error
The thing is, if you use the wrong one it completely changes the meaning of the sentence. There's no way you'd let a learner of English get away with saying "don't sit on this table" when you wanted "don't sit on this chair".
By the way, the rule is, you can have one letter wrong in a word but only if it doesn't make another legitimate word or another form of the same word. This is automated and there's no way to change it, except by adding "стол" as another correct answer which is not going to happen.