To improve the color you can load the pdfcolfoot
package.
But for the link there is currently no good solution. You are paying the price for the ability of pdftex to break links over lines and pages: To be able to do this it adds everything between start and end point to the link area, and this encompasses the text body.
A current texlive offers commands to interrupt a link, and for the header and footer there is code in the new PDF management which make use of them: https://tex.stackexchange.com/a/578405/2388.
But this can't be used easily for footnotes. In your example one can for example correct the link with
\documentclass[11pt]{book}
\usepackage{lipsum}
\usepackage[colorlinks]{hyperref}
\usepackage{pdfcolfoot}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@makecol
{\pdfcolfoot@current\unvbox\footins}
{\pdfcolfoot@current\pdfrunninglinkon \unvbox \footins \pdfrunninglinkoff}
{}{\fail}
\makeatletter
\begin{document}
\lipsum[2-5]\footnote{\hyperlink{target}{\lipsum[2-3]}}
\lipsum[2-3]
\newpage
\hypertarget{target}{THIS IS THE TARGET!}
%
\end{document}
But if the main text body contains also a link with a page break the link targets gets confused and the second part of the footnote links to the url:
\documentclass[11pt]{book}
\usepackage{lipsum}
\usepackage[colorlinks]{hyperref}
\usepackage{pdfcolfoot}
%
\usepackage{etoolbox}
\makeatletter
\patchcmd\@makecol
{\pdfcolfoot@current\unvbox\footins}
{\pdfcolfoot@current\pdfrunninglinkon \unvbox \footins \pdfrunninglinkoff}
{}{\fail}
\makeatletter
\begin{document}
\lipsum[2-3]
\footnote{\hyperlink{target}{\lipsum[1-4]}}%
\href{https://www.latex-project.org}{\lipsum[3-5]}%
\lipsum[2]
\newpage
\hypertarget{target}{THIS IS THE TARGET!}
%
\end{document}

So this is not a stable solution. I doubt that one can repair this in pdftex. In my opinion one will need luatex and new link code based on attributes.
Side remark: I quite loath documents with lots of large link areas. I'm often reading on a touch screen and it is a nuisance if one triggers a link when one only wants to scroll or to zoom.