If you have deleted pages and they no longer exist and your server returns 404, then WMT reporting is a normal situation and this is nothing to worry about. Consider this as a warning to you that the page does not exist in case the page *should* exist
, i.e. in case you have not deleted it or where you have deleted it by mistake.
If the page has existed and you have deleted it, it would be slightly better to return 410 Gone rather than 404 as it sends a clearer message to Google that the page is gone on purpose, and Google acts on this faster.
If the "linked from" pages show, but you know that there is no link any more from these "linked from" pages or the "linked from" page reported does not exist any more, this means that Google has not yet recrawled / attempted to recrawl this "linked from" page to see its new content/status and the report relies on the data Google has from the last time it crawled "linked from" pages.
If these "linked from" pages have a very low crawl priority in Google, Google may crawl them seldom and therefore you may see these pages as "linked from" in WMT for a long time.
Another usage of the WMT 404 report is that, if you see that you have a lots of external links (by checking "linked from") to a particular page that has been removed, and these links may have potentially been a source of traffic to your site, you may consider redirecting this URL to a similar page on your site (if you have similar page), to keep the traffic.
Alternatively, a very good custom 404 page which entices the visitor to continue browsing your site may also recover this traffic. So to summarise: If you have removed a page, and the request for this page now returns 404 (or 410), and you are NOT internally linking to these removed pages from within your own site, you should not worry about WMT 404 report.
submitting requests to big G to remove none existent pages off cache and search
Are you saying that these pages you have removed are still appearing in Google SERPs? Have you removed them long time ago or recently?
404 pages still in SERPs may happen when the page is newly removed - Google may keep it in SERPs for a little while just in case it was a "server blip" when Googlebot requested a page that resulted in 404.
This is why returning 410 is better when a page is removed - it tells Google that the page was purposely removed and Google is faster in removing it from its index - but it will still show it in WMT report.