Translation:The woman works out.
The emphasis here is on the exercise, not the woman. This sentence answer the question "Who is excersise?" The answers could be a woman, a man or even a dog (which is normal here in Duolingo:). If the answer is "The woman exercises", then the question should be "What is the woman is doing?". This is how I understand the difference between both annswers. Hope it help you and correct me if im wrong :)
There is no question "Who is exercise?" The question would be "Who exercises?" or "Who is exercising?", but the last is not the verb tense used here.
The last question has the verb "is" twice which is also wrong. The correct question would be "What does the woman do?" which is correct for this sentence to be an answer Another question would be "What is the woman doing?" and again the last one would give the answer "The woman is exercising."
If we're talking about the "Question" to the excercise:
If the question was "Who is exercising?" the answer would be the woman, putting more emphasis on her. Thus, I'd say 가 would be used for her instead of 는.
But, I think the 'question' for this duolingo exercise would better be "What is the woman doing?" which places more emphasis on the object of the sentence, the exercise. Thus, 는 is used here instead of 가.
You are correct in that the exercise is the focus of the sentence since 는 is used, but the OP's comment had nothing to do with where the emphasis was, neither did it indicate any. It was just a grammatical error.
No, a typo is not given if you change the conjugation of the verb or create another legitimate word. If you had written “worsk” or “wrks” that would have been a typo for “works”, but “woks” is another legitimate word so that would not be a typo either. The s is required on verbs for third person singular such as any one person that you are talking about.
Both "works out" and "exercises" are correct. However, the mobile app only gives word tiles for "works out".
And currently (2019 November), keyboard input for answering in Korean is only on Duolingo website, not mobile app.
Note also, the English verb in present tense for second person singular (he, she, it) adds the "s": Works out, exercises, talks.
Here are few that make additional changes: I do, she does; I have, she has; I am, she is.
As for articles in English, it can be "A" or "The". I do not see any definite clues in the sentence for one or the other.