Endnotes and headers

I’ve to put the endnotes at the end of each chapter. This is the code for a MWE:

documentclass[a4paper,12pt,twoside]{report}
usepackage[T1]{fontenc}
usepackage[utf8]{inputenc}
    usepackage{lipsum}

% notes
usepackage{endnotes}
renewcommandenoteformat{%
   noindenttheenmark. hangindent 0parindent%
}
usepackage{etoolbox}
preto{theendnotes}{%
  renewcommand{makeenmark}{textsuperscript{theenmark}enspace}%
}
renewcommand{notesname}{Note} % <-------------------------------------
letfootnote=endnote
usepackage{chngcntr}
counterwithin*{endnote}{chapter}

% headers
usepackage{emptypage}
usepackage{fancyhdr}
pagestyle{fancy}
fancyhf{}
setlength{headheight}{14.49998pt}
renewcommand{chaptermark}[1]{markboth{#1}{#1}}
renewcommand{sectionmark}[1]{markright{#1}}
renewcommand{headrulewidth}{0pt}
fancyhead[LE]{footnotesizescshapeMakeLowercase{rightmark}}
fancyhead[RO]{footnotesizescshapeMakeLowercase{leftmark}}
fancyhead[LO,RE]{thepage}

begin{document}
chapter{First chapter}
section{Section one}
lipsum[1-5]
footnote{lipsum[1]}
footnote{lipsum[3]}
section{Section two}
lipsum[2-7]
footnote{lipsum[2]}
section{Section three}
lipsum{1-5}
footnote{lipsum[8]}
footnote{lipsum[9]}
section{Section four}
lipsum{1-5}
footnote{lipsum[6]}
markboth{scshape note}{scshape note}
theendnotes
end{document}

Problem 1: in the header, “NOTE” appears not in scshape as well as the headers of the other pages.

Problem 2: I want to omit the title “Note” before the notes begin. But if I use renewcommand{notesname}{} I lack the header too, even if I put the code markboth{scshape note}{scshape note} before the command to print endnotes.
Maybe, the troubles are connected… thanx