I have done some testing and am unable to find any issues with Opera 9.52 on XP or Vista.

Moreover, I could not get to work the right hand mouse button DownloadStudio menu: on the Preferences screen in Opera, in Advanced tab, Toolbars section, there is no 'DownloadStudio menu'
Please make sure that opera is integrated correctly and the Opera menu options is checked along with the click monitoring plugins. If you go to the tools options dialog in DownloadStudio, try re-integrating into Opera. You should see a message that plugin settings have been changes successfully.

For example, rar files are not captures, while exe files are captured.
I have tested this and in my testing we are catching the correct mime types for RAR files. If you can post (or send a support email) the url of a RAR file which is not being caught I will take a look and ensure it is working. The url may have a strange mime type which we are not catching. You should be able to see the assocation between mime types and download method in the Opera advanced preferences. To check what mime type a url actually is you can paste the url into the DownloadStudio add job dialog and the mime type and file size will be displayed.

If there are still issues can you tell me what operating system are you using?
Have you, or do you have any other download managers integrated into opera?

I hope this information helps, let me know if there are still issues.