Check the wording of the ignoreLeadSection entry. [2nd sentence seems inaccurate?]

That's currently "A lead section is defined as content in an article with at least one heading that precedes the first heading". This seems to accurate to me, though it's a bit awkwardly phrased with how the concepts are grouped -- it should be read as "content in an-article-with-at-least-one-heading that precedes the first heading". The intention is to convey that if you view an article with no headings, this config setting won't apply to that.

Check the "Getting help" section. [Are "interface admins" actually needed for anything related to Edit Check, or just "admins"?]

You need someone with permissions to edit a .json file in the MediaWiki namespace. Exactly which set of people can do that will vary depending on wiki, I imagine...

Last week I went in and updated the generic config to feature all our new behaviors, as part of which I did reword the lead-section part: https://www.mediawiki.org/w/index.php?diff=8217012