Is it possible to show 403/404 messages on the front page? Is it possible to have - instead of a dedicated 403/404 page - just a custom div inserted into the front page? 'Cause when I think of what I'd like to show up at 403404, I want everything that the front page has. So, whatever the front page looks like over time, I would just want it to adopt a 403/404 message div.
You can make this with the following configuration and using Rules module.
1. create a page with a custom path ex, "404" and set this page as 404 on configuration -> site information
2. create a rule, if the request page its "404" then 
 2.1 system page redirect
 2.2 system show a message