Can 404 pages down your website rankings?

No, 404 pages do not effect to your website ranking....

404 pages don't impact to your website position.

Use 301 redirects rather than 302 redirects when redirecting URLs on a site to ensure ... Web pages that return 404 (File Not Found) for extended periods of time and that

No...404 pages does not affect your ranking because Google cannot crawl 404pages

404 can harm for website ranking and traffic, you should redirect to 404 page or home page by 301 redirection

I think No