The best way to download Korean dramas is to use an app that allows you to download them for free. You can find a variety of sites like - Viki, AnimeTV.to, Dramago, Kiss Asian etc.that offer different features, such as theatre mode, and they all offer some of the same basic features.
For more read - https://thetechwide.hpage.com/20-best-websites-to-watch-korean-drama-with-english-subtitles.html
https://educatorpages.com/site/techwide/pages/what-is-the-best-website-to-watch-korean-dramas
https://techwide.bookmark.com/where-can-i-download-korean-series