In order to manage access to user-defined questions, you have to keep it permanently in the dataset, otherwise it can be used only in this particular project by yourself (see Permanent vs project-scoped user-defined question).
After you share the question with a specific user or with the folder the defined question will appear on their question list.
To open manage access menu right-click on a user-defined question and select "Manage access" from the context menu. A new window will pop-up where you can see users and groups who currently have access to this item, delete them and add new.
