I would get the result of the output below
\documentclass[11pt, a4paper]{book}
\usepackage{geometry}
\geometry{%
papersize={19.7cm,27cm},
centering,
textwidth=380pt,
textheight=650pt}
\usepackage{fancyhdr}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\usepackage{tikz}
\parindent=0pt
\pagestyle{empty}
\begin{document}
\chapter{Title of chapter}
\section{and section}
Bla bla bla. In this page the pagestyle would be empty.
\newpage
\begin{tikzpicture}[remember picture,overlay]
\fill[lightgray] (-90pt,1cm) rectangle (0pt,2.5cm); %riquadro ad inizio pagina
\draw[gray] (-90pt,1cm)--(470pt,1cm); %linea sotto riquadro ad inizio pagina
\fill[lightgray] ({\textwidth/2-30pt},-23.45cm) rectangle ({\textwidth/2+30pt},-24.45cm); %riquadro per la pagina
\draw[gray] (-90pt,-23.45cm)--(470pt,-23.45cm); %linea di fondo pagina
\node at (0,1.25cm) [left]{\sffamily\chaptername\ \thechapter};
\node at (0,1.25cm) [right]{\slshape\sffamily\leftmark};
\node at (380pt,1.25cm) [left] {\slshape\sffamily author};
\node at ({\textwidth/2},-23.9cm) {\bfseries\sffamily\thepage};
\end{tikzpicture}
Here there is some text (here the number of the page is even);
\newpage
\begin{tikzpicture}[remember picture,overlay]
\fill[lightgray] (380pt,1cm) rectangle (470pt,2.5cm); %riquadro (destro) ad inizio pagina
\draw[gray] (-90pt,1cm)--(470pt,1cm); %linea sotto riquadro ad inizio pagina
\fill[lightgray] ({\textwidth/2-30pt},-23.45cm) rectangle ({\textwidth/2+30pt},-24.45cm); %riquadro per la pagina
\draw[gray] (-90pt,-23.45cm)--(470pt,-23.45cm); %linea di fondo-pagina
\node at (380pt,1.25cm) [right]{\sffamily\chaptername\ \thechapter};
\node at (380pt,1.25cm) [left]{\slshape\sffamily\leftmark};
\node at (0pt,1.25cm) [right]{\slshape\sffamily\rightmark};
\node at ({\textwidth/2},-23.95cm) {\bfseries\sffamily\thepage};
\end{tikzpicture}
And here there is some text too (here the number of the page is odd).
\end{document}
but on every page of the document. I already notice that there is a discussion about my question, but there I cannot obtain sufficient information on the use of everypage
package, or something that put me on the right track to solve this problem.
background
package sounds like it would be pretty useful herebackground
package documentation in order to realise how avoid these special pagesscrpage2
background
is the more useful option here; see the reasons in my answer below. By the way, I would suggest you to change the title of your question since, in its present form, it is misleading (you don't really want the formatting on every page).