Kentico has a lot of Global Events you can hook into, in the link below.
https://docs.kentico.com/display/K9/Reference+-+Global+system+events
You can also overwrite various Providers, but that isn't exactly a page / image / url request.
You may have to give a more case by case example though. If you need to really control page rendering, you may need to go with aspx+portal template, or pure aspx (not really recommended approach but gives the most power).
Does this help?