Here’s a list of each item referenced in the statistics, what it means, and where it comes from.
Google Page Rank:
This is Google’s proprietary calculation. Google does not provide an API to get the Page Rank but there are tools such as this to determine a Page Rank.
Sitemap:
The sitemap statistic is simply whether or not the site has a sitemap.xml file. It can be checked by looking for a domain.tld/sitemap.xml file. You can learn about these sitemaps at sitemaps.org.
Robots.txt
Much like sitemaps, this just checks for a domain.tld/robots.txt file. This is documented at robotstxt.org
Page Errors:
It’s hard to tell what page errors are as they could be any number of things.
Unreachable Pages: These are broken links. There are tools like W3C Link Checker that go through all the links on the page and make sure none return a 404 error. You can write a script that turns all the links on the page into an array or object and then use PHP or a command line tool like wget or curl to get the headers of the resource (link). Each time you count a 404 error you increment Unreachable Pages by one.
Domain Age & Domain Expiration: These can be found manually or pragmatically using a Whois search.
Hope this helps and good luck!
EDIT
There is a tutorial on how to write a broken links checker (“unreachable pages”) here.
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solved SEO – Unreachable pages [closed]