Hi Atexo,
first let me thank you for appreciation.
About the error trace, there's nothing strange if you find errors without referers,rather this is the normal condition. First you can check that alle these requests are real, just open your server's access log and check entries (filter by error and seach by timestamp), you will find the same requests.
Error trace feature was initially created to trace any strange request to site and have a simple panel to monitor these wrong requests easily. As example, there are a lot of bots / spiders that use common "patterns" to scan your site and search for flawed extensions, and you can find these requests.
Requests are logged as received by server so it is normal to have "encoded" chars (trace your browser requests and you will see this).
I suggest you to leave enabled and from time to time check for problems and urge the database. My way to check and fix is to sort by "hits" and fix the most requested errors.
As you can see from my image, the most requested pages comes without any referers, and if you see the URL structure you will easily understand they are searching for something (jce and a food.php script loaded in the images folder).
Kind regards,
Luigi