Making a private course public?
Sure, you can share your course from the Edit Course page. Just open the course, then click on the Edit Course under the menu button (three dots). On the edit course page you will be able to select lessons and change their status from Private to Shared.
Not sure what you are talking about. This seems to be a reoccurring problem that frustrates a lot of users. I may be wrong, but in the picture below there is no option to make the course public.
Additionally, I saw your comment from a few months back regarding the requirements for a public course. I understand why Lingq would want users to have the audio, a picture, and other details to make a public course, but that makes the process rather onerous to the community that is (more or less) responsible for generating new content. For example, I noticed the other week that there were no new publicly available Hebrew Courses. I saw one update the other day, but the requirements for a public course are preventing new content from being published. There has to be a middle ground.
It is getting to the point where I spend more time creating a lesson, making audio for that lesson, making sure that the audio is synced with the paragraph etc, than actually studying on Lingq. And for what? coins? learning?
Honesty, I don't see "many frustrated users" at all. Courses/lessons are shared by many people regularly every day.
Regarding the screenshot you attached, your first need to select a lesson/lessons you want to share. Just checkmark it and the option to change it's status will be available.
perhaps that was a bit of hyperbole, but when searching how to do it, there are more than a couple requests. Its not an attack, just feedback. I will definitely try your suggestion.