I've downloaded the AVG toolbar. I don't want any search engine box in it, but couldn't figure out how to remove it. Is there a way?
I'm pretty sure you can't. The only way would be to uninstall it: the search is built in to the toolbar.
There are alternatives to AVG, like avast which is much cleaner. McAfee SiteAdvisor also provides that "search safety ranking (green, yellow and red)" functionality.