No it's not ! you can add search bar and referal button in the 404 error page you can check the new google TOS to ensure yourself + you can see the hostgator default 404 error page you'll see a google search bar and firefox button.
Yes you can. You can even place Google Ads on error pages. When I first asked Google, they told me I am not allowed to. I then asked them again and showed them this thread: http://forums.digitalpoint.com/showthread.php?t=104815 Then they said it was alright. Peace,