That sounds like the textbook definition of a Relevant Link. Client makes mechanical parts, sells to mining & construction industry, links to/from mining & construction industry... not sure what would make that irrelevant. Google won't penalize you for those.

Normally the reports will let you know what page the error was encountered on and/or originated from. If there's an error listed there then odds are either the crawl found a broken link within your site that returned a 404 Not Found or you have something that was blocked returning a 403 Forbidden. Have you run any other crawls of the site (such as with Screaming Frog) or checked Google Search Console to see if there are any crawl errors listed on the site?

Since numerous search results pages are already in the index then Yes, you want to use the NoIndex tag instead of a disallow. The NoIndex tag will slowly lead to the pages being removed from the SERPs and the cache.

It is absolutely natural for people to link to your website with your URL. When looking at your backlink profile, you should see tons of links with the anchor text being things like your naked url or "website" or "this". In fact, it would be incredibly unnatural, and potentially a sign of paid linking schemes, if every single link to your website was a keyword rich, long tail anchor.