Why is there only one English language drop-down menu? How can I change to other languages?
Please forgot about this option. This is not the thing you're thinking about. This is not wpForo language changer. wpForo changes language automatically based on WordPress language. You can change WP language in WordPress Settings > General admin page. Also please read wpForo documentation:
https://wpforo.com/docs/root/translation/translate-using-pot-file/
I'm a WordPress Admin> Settings > General> Language
Changed to Korean.
However, only English appears in the drop-down menu.
How do I make the drop-down menu appear in Korean?
Please forget about this option. This doesn't have any relation to forum language. This is a XML translation function mode. You don't use that so don't check this option anymore. Also please don't duplicate the same question in many topics.
If you changed WP language wpForo already loaded on that language. You can see buttons and other parts are already in Korean language. If some phrase is not translated you should edit the Korean translation file of wpForo and complete the translation. The Korean translation file is not complete. Also you can translate all phrases using the Dashboard > Forums > Phrases system. Search for the phrase, edit and change the value.
Please read the doc and complete translation.
Use Korean translation file:
https://wpforo.com/docs/translation/translate-using-pot-file/
Use wpForo Phrase system:
https://wpforo.com/docs/translation/quick-translation-phrases/
General information how to translate wpForo: