Using site: query to test indexing of your page(s)? Read this!

Question

First and foremost it should be noted that a 'site:' query is not a reliable way to test indexing.

There are a number of ways a URL can still appear in search results, but NOT show in a site query. 
A site: query is still just a glorified 'keywords' query. And as such keyword searches are designed to find some good matches, rather than be a comprehensive list of all matching. In particular Google filters and hides duplicates (to avoid cluttering results with lots of occurrences of the 'same' thing) 
So if just run general site query like site:example.com will generally get SOME matches from example.com rather than all. Often substantially less than all!
(and also the 'about 123 results' indication, is just an estimate. It not intended to be accurate. Can both under or over estimate)
Also things like personalized search and safe-search means pages aren't visible to one person searching. While someone else might see matches. 
Finally there some edge cases around indexing of alternate and non-canonical URLs, particularly involving hreflang. A page can be found via its alternate URLs with site:, so even though a page NOT indexed, it appears in search results with site: query. 
Use the Search Console for more accurate indication. The Page Indexing/Coverage report shows an accurate list total of indexed pages. Although it can be outdated, its typically showing a snapshot last updated a few days ago. 
You can use a site: query to test indexing of a single page, subject to some limitations. It matches from the 'middle'. 
The protocol is ignored - will always search http+https even if specify one in query
Not case sensitive. Matches letters/numbers, not symbols. eg - and / are interchangeable.
It automatically includes subdomains. [site:example.com/page, will match www.exmaple.com/page AND example.com/page] does not work in reverse. site:www.example.com will NOT match http://example.com!
Will match paths, including partial. So can search site:example.com/folder/page or site:example.com/folder to match www.example.com/folder/page or even www.example.com/folder/page.html and www.example.com/folder/page-second.php
Does NOT match the query string, so bits after ? are IGNORED. Searching site:example.com/page?color=red WILL actually match www.example.com/page?color=blue
Use the 'inurl:' operator for much more precise matching of the URL. Can match anywhere, an will match against the protocol and the query string. And doesnt automatically include subdomains. But still effectively a 'contains' query, rather than needing to match the whole URL.