Just to confirm: The same downloads work in other browsers?
When other browsers work, then try to change the downloads-folder (or enable "Ask where to save the downloaded file": There could be a permission problem and Opera cannot write to the Downloads folder. Saving the files to the Desktop might work. Or check the settings "System Preferences > Security > Privacy > Files and Folders". Make sure Opera has access to the Downloads folder.
Or maybe you have a download-manager addon/app that tries to take over those downloads but fails (likely due to permission problems)
Hope this gives you some ideas and helps to solve that problem 🙂