404 page and customization of this

Hi

I’d like to change my 404 page on WP2. When users look forsomehting not there, they get the 404. Is there any way I can capture the word, url og ??? they used to get to (search) my site ?

I’d like to end up with something like this:

“I’m sorry, you searched for <SUBJECT> or <URL>, but unfortunately .. bla bla bla”

And… I’d also like to add a presearch on the 404 page. So that If they searched for https://www.boyer-draeby.dk/SUBJECT, I’d presearch and present a search on “SUBJECT” on my 404 -page.

How much information can I get from users request when they hit my 404-page ?

Cheers
Jakob
https://www.boyer-draeby.dk