The Duolingo answer is right of course, but in English you would nearly always say 'table and chair' with the table first. The phrase 'chair and table' is most unusual. It is similar to other common pairings with a well-established word order - other examples are 'knife and fork', 'bucket and spade' and 'black and white'. If you reverse the usual order, then the phrase remains grammatically correct but sounds unnatural (in UK English).
That's possible, but we have to make sure that the learner knows which is which. Imagine the problem in Russian, where the words for table and chair differ by only one letter ;)
I would say "stół i krzesła" (a table and chairs) definitely, but one chair and a table... I don't feel anything more idiomatic here, in Polish.