The plumbing: robots.txt, canonicals, hreflang, sitemaps, redirects and response headers.
Generate a correct robots.txt with crawl rules and sitemap.
Generate hreflang tags for multi-language / multi-region pages.
Create canonical link tags to prevent duplicate-content issues.
Build meta robots directives (index/follow, max-snippet…).
Generate an XML sitemap from your list of URLs.
Build .htaccess 301/302 redirect rules.
Trace redirect chains and spot wasteful hops.
Inspect a URL's HTTP response headers.
Visitors rarely see technical problems, but those problems decide which URLs search engines crawl, which version they index and which language they show. Six of these tools write code you paste into your site, and two read what your server already sends.
A page blocked in robots.txt cannot be crawled, so search engines never see a noindex tag on it. If you want a page out of the index, let it be crawled and use noindex. The sitemap generator leaves lastmod out by default, and any date you pick applies to every URL, so add one only when it is the real date those pages changed. For the two checkers, pasted curl output gives the full result and stays in your browser; the quick live check sends your URL to a public proxy and shows only part of the picture.