Ok, first, does the url with /errors/error_404 (without the query string) exist?

Also - are you using something to create your 404 pages for tracking purposes?

The query string on the url would appear to be stating the referring url anyway - hence ?q=-i3 basically equates to the page /i3

At a guess - it could be there is a script running to create logs on specific 404's, or create a new log each time one occurs - if this folder is visable to the crawlers, it would get spidered and subsequently the problem would arise.

It does, when you get the report, filter column D marked "4XX (Client Error)" and you will see your 404's there - further along in the report you will also be able to see referring url which will show you which page is linking to it.

Custom crawl right here on SEOmoz, or you could use Xenu

SEO advantage I would suggest is negligible, if any in this case - more a case of aesthetics as has been suggested, as well as character count saving.

Section pages I would go with "Section | Company Name"

Product pages I would go with "Product - Section | Company Name"