Which Are the Standard W3C Meta Tags

Has the W3C ever published a standard set of meta tags?

They are trying in HTML 5.

The attempt is, however, laughable:

Extensions to the predefined set of metadata names may be registered in the WHATWG Wiki
MetaExtensions page. [WHATWGWIKI]

Anyone is free to edit the WHATWG Wiki MetaExtensions page at any time to add a type.

Is there a W3C standard meta tag to determine the cover image used to represent a website?

W3C「Manifest for a web application」draft standard

The (new) standard that’s closest to what’s described in this question is a specification called Manifest for a web application (aka Application Manifest):

This specification defines a JSON-based manifest that provides developers with a centralized place to put metadata associated with a web application: the web application's name, links to icons, as well as the preferred URL to open when a user launches the web application.…

The example JSON manifest below shows how to specify a set of icons as well as a set of one or more splash screens and other properties for an application.

Example manifest

{
  "lang": "en",
  "name": "Super Racer 2000",
  "short_name": "Racer2K",
  "icons": [{
        "src": "icon/lowres",
        "sizes": "64x64",
        "type": "image/webp"
      }, {
        "src": "icon/hd_small",
        "sizes": "64x64"
      }, {
        "src": "icon/hd_hi",
        "sizes": "128x128",
        "density": 2
      }],
  "splash_screens": [{
        "src": "splash/lowres",
        "sizes": "320x240"
      }, {
        "src": "splash/hd_small",
        "sizes": "1334x750"
      }, {
        "src": "splash/hd_hi",
        "sizes": "1920x1080",
        "density": 3
      }],
  "scope": "/racer/",
  "start_url": "/racer/start.html",
  "display": "fullscreen",
  "orientation": "landscape",
  "theme_color": "aliceblue",
  "background_color": "red"
}

To associate a manifest with a Web application/document, you use <link rel=manifest>:

Example of how to associate a Web app/document with a manifest

<!doctype>
<html>
<title>Store finder - search</title>

<!-- Startup configuration -->
<link rel="manifest" href="manifest.webmanifest">

<!-- Fallback application metadata for legacy browsers -->
<meta name="application-name" content="Store Finder">
<link rel="icon" sizes="16x16 32x32 48x48" href="lo_def.ico">
<link rel="icon" sizes="512x512" href="hi_def.png">
…

It’s a relatively new spec and still in the process of being refined and implemented in browsers, so it’s not an immediate solution to the problem in the question here. But the authors are from Mozilla and Google, along with Intel, and I think you can expect to see support for it getting added at least to Firefox and Chrome in the near future; there are feature bugs open for both browsers:

(webmanifest) [Meta] Implement Web Manifest spec in Gecko
Implement Web Application Manifest [in Chrome]

Suggested meta tags for HTML 5 that should be considered a must have

There is no such thing as minimum meta tags (unless of course I got your question wrong). As far as I am aware no meta tag is required and the ones you add are the ones for your specific needs.

Consider the following document:

<!DOCTYPE HTML>
<html>
    <head>
        <title>Some Title</title>
    </head>
    <body>

    </body>
</html>

You can validate it and not get any warning whatsoever. The validator just reminds you that the default encoding is missing. This is not even a warning, just an information.

The working draft has this to say about meta tags:

The meta element represents various kinds of metadata that cannot be expressed using the title, base, link, style, and script elements.

And it goes on:

4.2.5.1 Standard metadata names

application-name, author, description, generator, keywords

Further it mentions some additional tags concerning a page's status, contextual representation and character encoding.

Although none of these ar explicitly required by the standard, there are in fact best practices, especially concerning search engine optimization (SEO). This has nothing to do with the HTML standard but with web (search) crawlers.

You can get some good advice which meta tags matter (for Google) at the Webmaster Tools meta tag support page

What meta tag should I use to indicate the website (not content) author?

Guess it's the typesetter!

I use three things:

a humans.txt file
If the site gives permission, a link in the footer to my site "Web design by …"
A x-author: My Business Name header sent with the php.

The last one is a little pointless, but it's more there so a future developer who takes over might be able to have a clue who I am!

Where can a list of all existing HTML meta tags be found? (DUBLIN CORE, OPEN GRAPH etc)

for example where can I find a list of all possible meta tags that start "citation_"?

https://wiki.whatwg.org/wiki/MetaExtensions lists about 20 "citation_" keywords.

I am struggling to locate a definitive list of all possible meta tag schemas and for each schema a list of all possible tags.

There are currently 356 meta keywords listed on the wiki page cited above.

As far as how definitive that list is, it’s the resource that the HTML spec itself cites:

Also, before creating and using a new metadata name, consulting the WHATWG Wiki MetaExtensions page is encouraged — to avoid choosing a metadata name that's already in use, and to avoid duplicating the purpose of any metadata names that are already in use, and to avoid new standardized names clashing with your chosen name. [WHATWGWIKI]