What can be put in 'Full HTML' node/fields? The obvious answer to this question is HTML code of course, but my deeper question is, is this an HTML body content-like HTML? I suppose I can't put HTML header content-like HTML? Correct? I mean I can't put META tags for example.
You technically can use &lt;meta&gt; tags, since they will not be stripped out of the content that you place into a textfield that uses the default "full HTML" input filter. However, this content will be output in the &lt;body&gt; of the HTML document, which means using &lt;meta&gt; tags here will cause invalid HTML and most likely be ineffectual. 

If you are looking for a way to customize the &lt;meta&gt; tags used on your Drupal site, there are many modules available to help with this. The Meta Tags module is the most popular, but that project's page also lists some other meta tag-related modules.