We have redirected all non-existing pages to home page. It was fine for some days.
That's a bad idea because if search engines indexed all those now non-existing URLs that were working several days ago (or whenever the links did work), then people who use the search engines will be misled because they will show what is in their cache to describe the page, and theres likely a huge difference between a home page and the now non-existing pages.
Few days back i saw increase in the number of soft 404 errors for desktop. And the errors were the page urls that have been redirected to the home page. After fixing all the soft404 for desktop, i found increase in soft 404 errors for smartphones. what it would mean ?
Soft-404's is something to describe a page containing a message similar to what a real 404 page returns except that the status code returned is 200 when it should be 404. Try to revise your pages that google sees as soft-404's so that you don't have words like "not found" or "not available" near the beginning of your page and try to add a good amount of content to the page.
Is there any option to remove the non-existing urls in GWT.
Figure out what links you really don't want to have reported, and if you're happy with google no longer indexing those links as well, then apply an HTTP status "410 Gone" to those links. Here's PHP code that will help you.
header("HTTP/1.1 410 Gone",true);
?><!-- insert any HTML code here --><p>This page doesn't exist</p>
However if those links can be reused, you definitely should give them an HTTP status "301 Moved Permanently" with the location pointing to the new URL.