Subject: bug#15839: 24.3.50; `isearch-allow-scroll': be able to scroll point off screen temporarily

From: Juri Linkov <[email-masked]>
Date: Sun, 25 Nov 2018 22:15:23 +0200

> What counts is the user perspective: scrolling should show all
> hits highlighted, no matter how far you scroll and no matter
> which directions.  And to get that behavior a user should not
> need to change option `lazy-highlight-buffer'.  That option
> should have no effect on this behavior, and vice versa.

The first part of your request is already implemented as well:
you can customize `search-exit-option' to the value `nil'
(its tag text is "Don't terminate incremental search"),
then it works exactly like you want.