The rule applies to the content you end up seeing after your browser follows all automatic redirects and possibly even interstitials (ads/disclaimers). Redirects are an irrelevant technical detail in this context.

A quick search seems to indicate that yes, you might be responsible for linking to the altered content. As a website author you have - in principle - a duty to check what you are linking to. It is unclear what that means in practice. I would guess that it would involve a test if timely detection of alteres content on the linked site would have imposed an undue burden. The only part that is absolutely certain is that a website owner must react if they are notified that they are linking to illegal content. Other than that, it's seemingly a grey area.

Guess why the remaining search engines are so good at classifying certain types of sites of the "adult entertainment" and and other such types?

I am not sure if the courts distinguish between automatically generated pages and authored/curated content that involves human input in its creation. Courts haven't been exactly consistent on these points.

Plenty of times. Have you ever seen a notice from Google referencing chillingeffects.org at the end of your search results?

Yes, I remember a high profile German tech news site involved in at least one such legal battle. If memory serves, it revolved around a link to Alcohol 120%, a tool to rip copy protected disks. The news site lost the case, I think.