I analyzed our website landing pages, there are pages to our search results, which do not have any result. Only shows "watch other items". It means visitor used our search field and tried to find something what we don't have on the website. There are also no links on the website to his search term.
So my question is can google index these pages in which visitor comes while browsing our website? example: www.website.com/search/nonexistingproduct
Such pages are started to give us visitors from google search results.
The reason i am asking is that we are planning to start mobile website and redirect visitors from desktop website www.website.com/search/results1 to m.website.com/search/results1. So if there are no such pages on desktop website then mobile will not have either. So after pressing on google results on 'nonexistingproduct' and the redirect to mobile version, we will have this page m.website.com/search/nonexistingproduct?
I doubt Google used a visitors internet browser history. A spam bot could have posted the link somewhere and Google could have followed it.
You should remember that Google has a number of products like the Google toolbar that tracks things (along with analytics, AdSense, etc..) so if any of these things are on that page Google knows the page exists.
You could use a meta tag to noindex your search results or at least the pages that do not have anything on them yet.
o my question is can google index these pages in which visitor comes while browsing our website? example: www.website.com/search/nonexistingproduct
Google can and will index absolutely everything. Even when it doesn't particularly want to, as in the case of internal search-result pages. Indexing is like an addiction for them; they can't look at a page and say "Thanks but no thanks".
So you have to make sure that any page produced by your site search has an unambiguous "noindex" header.