When you perform a search like [site:nameofthewebsite.it], Google shows the resources of the website in no specific order. If it’s true that, generally, on top of the list you will find the homepage, it’s not true that the other resources are listed in order of importance.
Many years ago it was possible to use a hack to see all the resources from the search engine in order of PageRank, but this function was eliminated by Google a long time ago.
Until a few years ago, webmasters could use the “noindex” instruction to request that Google does not index a page. Usually this instruction was given through a metatag called “robots” in the <head> part of a page.
Google would not index a page where it found the tag “noindex”. This meant Google was not adding to its index any link between the words in the page and the page itself (as happens in a book index). Without indexing, the user was not able to find the page with a query to the search engine.
A Google penalty is a punishment given to a website that has acted against the search engine’s webmaster guidelines.
It’s not against webmaster guidelines to have 404 errors in a website. Therefore there is no penalty related to 404 errors, and Google has confirmed this many times.
One of the more fascinating examples of smoke and mirrors in SEO is the idea of a formula to decide how often a keyword or phrase should be repeated within a page to increase the page’s relevancy to that word or phrase.
Documentation about information retrieval (the discipline that explain how search engines work) shows that the formulas used by search engines to calculate the relevancy between keywords and documents are far more complex than those invented by SEOs.