"여자는 책을 손으로 씁니다."
Translation:A woman writes the book down by hand.
I tend to agree. In English, the idiom "write down" is used to mean write something that already exists (e.g. I write my teacher's instructions--the instructions already existed), not to compose something new. I could see "down" being used here if the woman already composed the book in her head before writing it down, or if she was listening to an audiobook and decided to write it down for some reason, but those are unlikely scenarios, and in most contexts, we wouldn't use "down" to translate this sentence.
I think the combination of "순으로" (by hand) and "씁니다" (to write, instead of "작다", which is also to write) means that the woman is copying the book by hand. "씁니다" is apparently like writing brainlessly and w oh thout creativity (like copying something thats already written), and "씁니다" is like thinking while you write (a song or a long message to someone thats not just "coming home; be there in 10"
It might not be entirely correct to use the word down as far as the actual ords in the Korean sentence, but if they mean the woman is writing a book by hand, then the meaning is the same to use the word down. It's the sam either way. Some would add the word, others wouldn't.
The connotation of "write [s.th] down" fits better with the connotation of 전다, I feel. You write down lecture notes, phone numbers, recipes, etc, things that don't require a lot of effort or creative thought at the moment lf writing. A book is simply written; "a woman writes the book by hand" both feels better to an English speaker and more precisely translates the Korean sentence. The phrase "write [s.th] by hand" already shows clearly the thing written is handwritten, adding "write down" into the mix is redundant and sounds clunky to a native speaker.
By all means correct me on the Korean but . . .
"A woman writes the book by hand." "여자는 책을 (기계에 의해 아니고) 손으로 씁니다." (directly, not by machine)
"A woman writes the book with hand." "여자는 책을 (손을 버리지 않고) 손으로 씁니다." (not without hand)
"A woman writes the book with her hand." "여자는 책을 (발로보다는) 손으로 씁니다." (not with her foot, say)
The sense of 'with' that's the same as 'by' in English always takes a determiner. Without a determiner it's more of the sense of including. As it's a body part here it would be strange with 'a' or 'the'; only the personal pronoun 'her' is accepted (or maybe 'one' as opposed to two hands, etc). That's why we have to use 'by hand' instead (and I've wasted too much time online futilely trying to search for any explanation of when to use 'with' with or without a determiner) . . .
No, 는/은 and 가/이 do not have direct counterparts in English, and Korean doesn't have articles like "the" or "a/an". 는/은 marks the conversational topic and 가/이 marks the subject of the sentence.
If you're referring to a specific woman, you could use 이 "this", 그 "that (near you)", or 저 "that (over there)" before 여자, or if you're talking about a group of women you could use 여자들. Either way you would still need to use 는/은 or 가/이 to mark which nouns in the sentence are doing what.