Translation:The woman wants to write this book by herself.
When is "tự mình" used and when is just "tự used? "Anh ấy tự nấu ăn" (He cooks food by himself) was an accepted Duolingo answer for another question, so are "tự mình" and "tự" both used for by him/her-self?
Not really but cuốn is more popular in the Southern dialect while quyển sách is more popular in the Northern. From an etymological point-of-view, cuốn is an earlier borrowing from Chinese.