Questo esempio minimo dà un risultato che credo sia quello che vuoi ottenere (salvo la doppia riga nell’intestazione…)`\documentclass[a4paper]{book}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english, italian]{babel}
\usepackage{fancyhdr,lipsum,emptypage}
\newenvironment{abstract} %
{\cleardoublepage\null \vfill\thispagestyle{plain}%modificato
\begin{center} %
\bfseries \abstractname \end{center}} %
{\vfill\null}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{}
\fancyhead[LE,RO]{\scshape\thepage}
%\fancyhead[LO]{\scshape\footnotesize\nouppercase{\rightmark}}
\fancyhead[LO,RE]{\scshape\footnotesize\nouppercase{\leftmark}}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}
\addtolength{\headheight}{1.6pt}
\begin{document}
\tableofcontents
\markboth{\abstractname}{\abstractname}
\addcontentsline{toc}{chapter}{\abstractname}
\begin{abstract}
Versione del sommario in italiano
\end{abstract}
\selectlanguage{english}
\markboth{\abstractname}{\abstractname}
\addcontentsline{toc}{chapter}{\abstractname}
\begin{abstract}
english
\end{abstract}
\selectlanguage{italian}
\chapter{PRIMO}
\lipsum
\end{document}`