Any value alongside Search 404

Problem/Motivation

Please forgive my ignorance if this is a really stupid question!

My understanding

I think I get that out-of-the-box, this module will seriously speed up response time for situations where (for example), I have a some simply Body text with an embedded <img> tag that basically points to 'nowhere' - i.e. is a broken link and will result in a 'Not found (404)' as inspected in the browser...

My understanding is that, without additional tweaks in the settings.php, that's all it does, albeit a great thing!

Search 404

I use the Search 404 → module to redirect users to a 'helpful' suggestions page when they attempt to visit a URL which does not match any recognised Drupal path.

My question

My question is about whether the following three assertions are correct...

With the out-of-the-box Fast404 behaviour (i.e. simple file extensions only):

1. These two things are considered to be completely separate in nature.
2. Using Search API has no negative effect on the out-of-the-box behaviour of Search404
3. My site still benefits from having Fast404 active in terms of delivery of the Drupal pages.

Have I got the gist of it right?