Logged data is stored exclusively on your computer. To search logged data select date and time, program user and log type. If mandatory user mode is off use "[EVERYONE]" to see logs. You can also search logs by url (partial strings supported) and user/ip. Because of the way MITB mode works, you may see many log entries for the same object: this is absolutely normal because, during download or upload, data gets split across multiple requests.
To view/modify categories of an URL, select the row from main window data list and click on button Modify or double click the selected row. The view/modify window is divided in 3 parts. The bottom one displays the request. The left one displays in which categories the url and its parts are inserted. On the right one we find the categories list. To add a category to URL/HOST/DOMAIN just select it from the left pane and double click the selected value in the right pane. To remove a category or operate on the whitelist archive double click on category in the left pane. Please keep in mind that you can't remove a category if it's coming from the external service.