How to exclude some slides from numeration, delete slide numbers and delete circles?

Question

I would like to

(1) exclude the Appendix section from the numeration of the main slides

(2) hide the numbers at the bottom of the slides belonging to the Appendix section

(3) hide the circles at the top of the slides belonging to the Appendix section

How can I do it?

Here an example of my document: as suggested in the comments below I can reach (1) by including [noframenumbering]. However this does not solve (2), (3)

\documentclass[xcolor=dvipsnames]{beamer}

\usetheme{Antibes}
\usecolortheme{dolphin}
\usefonttheme{professionalfonts}
\useoutertheme{infolines}
\useinnertheme{circles}

\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{etoolbox}
\usepackage[gen]{eurosym}

\makeatletter
\newcount\beamer@subsectionstartframe
\beamer@subsectionstartframe=1
\apptocmd{\beamer@subsection}{\addtocontents{nav}{\protect\headcommand{%
            \protect\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}{}{}
\apptocmd{\beamer@subsection}{\beamer@subsectionstartframe=\c@framenumber\advance\beamer@subsectionstartframe by1\relax}{}{}
\AtEndDocument{\immediate\write\@auxout{\string\@writefile{nav}%
        {\noexpand\headcommand{\noexpand\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}}{}{}
\def\beamer@startframeofsubsection{1}
\def\beamer@endframeofsubsection{1}
\def\beamer@subsectionframes#1#2{%
    \ifnum\c@framenumber<#1%
    \else%
    \ifnum\c@framenumber>#2%
    \else%
    \gdef\beamer@startframeofsubsection{#1}%
    \gdef\beamer@endframeofsubsection{#2}%
    \fi%
    \fi%
}
\newcommand\insertsubsectionstartframe{\beamer@startframeofsubsection}
\newcommand\insertsubsectionendframe{\beamer@endframeofsubsection}
\makeatother

\newcounter{subsectionframenumber}
\newcounter{totalsubsectionframenumber}

\setbeamertemplate{headline}
{
    \leavevmode%
    \hbox{%
        \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,right]{section in head/foot}%
            \usebeamerfont{section in head/foot}\insertsectionhead\hspace*{2ex}
        \end{beamercolorbox}%
        \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,left]{subsection in head/foot}%
            \parbox[b]{.4\textwidth}{
            \usebeamerfont{subsection in head/foot}\hspace*{2ex}\insertsubsectionhead%
            \setcounter{subsectionframenumber}{1}
            \addtocounter{subsectionframenumber}{\insertframenumber}
            \addtocounter{subsectionframenumber}{-\insertsubsectionstartframe}
            \setcounter{totalsubsectionframenumber}{1}
            \addtocounter{totalsubsectionframenumber}{\insertsubsectionendframe}
            \addtocounter{totalsubsectionframenumber}{-\insertsubsectionstartframe}
            \ifnum\thesection>0%
            \foreach\x in {1,...,\thetotalsubsectionframenumber}{%
                \ifnum\x=\thesubsectionframenumber%
                \usebeamertemplate{mini frame}~%
                \else%
                \usebeamertemplate{mini frame in other subsection}~%
                \fi%
            }%
            \fi%
        }%
        %\hfill\hyperlink{toc}{Outline}%
        \end{beamercolorbox}}%
        \vskip0pt%
    }
\usepackage{bbm}
\usepackage{amssymb}
\usepackage{mathabx}

\newcommand{\beginbackup}{
   \newcounter{framenumbervorappendix}
   \setcounter{framenumbervorappendix}{\value{framenumber}}
}
\newcommand{\backupend}{
   \addtocounter{framenumbervorappendix}{-\value{framenumber}}
   \addtocounter{framenumber}{\value{framenumbervorappendix}} 
}

\usepackage{multicol}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}


    \beginbackup
    \begin{frame}
        \titlepage
    \end{frame}
    \backupend

    \begin{frame}[label=toc]
        \frametitle{Outline}
        \tableofcontents
    \end{frame}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \section{BLAH}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \subsection{sub1}

    \begin{frame}{SLIDE1}\label{slide1}
    \hyperlink{appendix}{\beamergotobutton{More}}
    \end{frame}

    \begin{frame}{SLIDE2}
    \end{frame}


    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \section{Appendix}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{frame}[noframenumbering]{Extensions 1}\label{appendix} 
    \end{frame}
    \begin{frame}[noframenumbering]{Extensions 2}
    \hyperlink{slide1}{\beamergotobutton{Back}}
    \end{frame}



\end{document}

Answer 1

The code is getting a bit messy, seems to fulfil (1)-(3). I also removed the frame numbers displayed on the titlepage, as you seem to want this unnumbered it became 0/3 and looked strange.

\documentclass[xcolor=dvipsnames]{beamer}

\usetheme{Antibes}
\usecolortheme{dolphin}
\usefonttheme{professionalfonts}
\useoutertheme{infolines}
\useinnertheme{circles}

\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{etoolbox}
\usepackage[gen]{eurosym}

\makeatletter
\newcount\beamer@subsectionstartframe
\beamer@subsectionstartframe=1
\apptocmd{\beamer@subsection}{\addtocontents{nav}{\protect\headcommand{%
            \protect\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}{}{}
\apptocmd{\beamer@subsection}{\beamer@subsectionstartframe=\c@framenumber\advance\beamer@subsectionstartframe by1\relax}{}{}
\AtEndDocument{\immediate\write\@auxout{\string\@writefile{nav}%
        {\noexpand\headcommand{\noexpand\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}}{}{}
\def\beamer@startframeofsubsection{1}
\def\beamer@endframeofsubsection{1}
\def\beamer@subsectionframes#1#2{%
    \ifnum\c@framenumber<#1%
    \else%
    \ifnum\c@framenumber>#2%
    \else%
    \gdef\beamer@startframeofsubsection{#1}%
    \gdef\beamer@endframeofsubsection{#2}%
    \fi%
    \fi%
}
\newcommand\insertsubsectionstartframe{\beamer@startframeofsubsection}
\newcommand\insertsubsectionendframe{\beamer@endframeofsubsection}
\makeatother

\newcounter{subsectionframenumber}
\newcounter{totalsubsectionframenumber}

\setbeamertemplate{headline}
{
    \leavevmode%
    \hbox{%
        \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,right]{section in head/foot}%
            \usebeamerfont{section in head/foot}\insertsectionhead\hspace*{2ex}
        \end{beamercolorbox}%
        \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,left]{subsection in head/foot}%
            \parbox[b]{.4\textwidth}{
            \usebeamerfont{subsection in head/foot}\hspace*{2ex}\insertsubsectionhead%
            \setcounter{subsectionframenumber}{1}
            \addtocounter{subsectionframenumber}{\insertframenumber}
            \addtocounter{subsectionframenumber}{-\insertsubsectionstartframe}
            \setcounter{totalsubsectionframenumber}{1}
            \addtocounter{totalsubsectionframenumber}{\insertsubsectionendframe}
            \addtocounter{totalsubsectionframenumber}{-\insertsubsectionstartframe}
            \ifnum\value{section}>0%
            \foreach\x in {1,...,\value{totalsubsectionframenumber}}{%
                \ifnum\x=\value{subsectionframenumber}%
                \usebeamertemplate{mini frame}~%
                \else%
                \usebeamertemplate{mini frame in other subsection}~%
                \fi%
            }%
            \fi%
        }%
        %\hfill\hyperlink{toc}{Outline}%
        \end{beamercolorbox}}%
        \vskip0pt%
    }
\usepackage{bbm}
\usepackage{amssymb}
\usepackage{mathabx}

\newcounter{framenumbervorappendix}

\usepackage{multicol}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

{

  \setbeamertemplate{footline}{
    \leavevmode%
    \hbox{%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
      \usebeamerfont{author in head/foot}\insertshortauthor
    \end{beamercolorbox}%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
      \usebeamerfont{title in head/foot}\insertshorttitle
    \end{beamercolorbox}%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
      \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
%      \insertframenumber{} / \inserttotalframenumber\hspace*{2ex} 
    \end{beamercolorbox}}%
    \vskip0pt%
  } 

    \begin{frame}[noframenumbering]
        \titlepage
    \end{frame}

}

    \begin{frame}[label=toc]
        \frametitle{Outline}
        \tableofcontents
    \end{frame}

    \section{BLAH}
    \subsection{sub1}

    \begin{frame}{SLIDE1}\label{slide1}
    \hyperlink{appendix}{\beamergotobutton{More}}
    \end{frame}

    \begin{frame}{SLIDE2}
    \end{frame}


    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     \setcounter{framenumbervorappendix}{\value{framenumber}}
    \section*{Appendix}
    \subsection{Appendix}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 {

 \setbeamertemplate{headline}
 {
     \leavevmode%
     \hbox{%
         \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,right]{section in head/foot}%
             \usebeamerfont{section in head/foot}\insertsectionhead\hspace*{2ex}
         \end{beamercolorbox}%
         \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,left]{subsection in head/foot}%
         \end{beamercolorbox}}%
         \vskip0pt%
     }   

  \setbeamertemplate{footline}{
    \leavevmode%
    \hbox{%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
      \usebeamerfont{author in head/foot}\insertshortauthor
    \end{beamercolorbox}%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
      \usebeamerfont{title in head/foot}\insertshorttitle
    \end{beamercolorbox}%
    \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
      \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
%      \insertframenumber{} / \inserttotalframenumber\hspace*{2ex} 
    \end{beamercolorbox}}%
    \vskip0pt%
  }   


    \begin{frame}{Extensions 1}\label{appendix} 
    \end{frame}
    \begin{frame}{Extensions 2}
    \hyperlink{slide1}{\beamergotobutton{Back}}
    \end{frame}


}

\setcounter{framenumber}{\value{framenumbervorappendix}}

\end{document}

Answer 2

If you change the \AtEndDocument... line to

\pretocmd\appendix{\immediate\write\@auxout{\string\@writefile{nav}%
{\noexpand\headcommand{\noexpand\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}}{}{}

then you will not get circles for the sections etc. in the appendix. Using samcarter's suggestion of [noframenumbering] you can avoid the title page getting a number without resorting to fiddling the counters.

However, I'm not altogether convinced I understand the aim here.

\documentclass[xcolor=dvipsnames]{beamer}
\usetheme{Antibes}
\usecolortheme{dolphin}
\usefonttheme{professionalfonts}
\useoutertheme{infolines}
\useinnertheme{circles}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{etoolbox}

\makeatletter
\newcount\beamer@subsectionstartframe
\beamer@subsectionstartframe=1
\apptocmd{\beamer@subsection}{\addtocontents{nav}{\protect\headcommand{%
      \protect\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}{}{}
\apptocmd{\beamer@subsection}{\beamer@subsectionstartframe=\c@framenumber\advance\beamer@subsectionstartframe by1\relax}{}{}
\pretocmd\appendix{\immediate\write\@auxout{\string\@writefile{nav}%
    {\noexpand\headcommand{\noexpand\beamer@subsectionframes{\the\beamer@subsectionstartframe}{\the\c@framenumber}}}}}{}{}
\def\beamer@startframeofsubsection{1}
\def\beamer@endframeofsubsection{1}
\def\beamer@subsectionframes#1#2{%
    \ifnum\c@framenumber<#1%
    \else%
    \ifnum\c@framenumber>#2%
    \else%
    \gdef\beamer@startframeofsubsection{#1}%
    \gdef\beamer@endframeofsubsection{#2}%
    \fi%
    \fi%
}
\newcommand\insertsubsectionstartframe{\beamer@startframeofsubsection}
\newcommand\insertsubsectionendframe{\beamer@endframeofsubsection}
\makeatother

\newcounter{subsectionframenumber}
\newcounter{totalsubsectionframenumber}

\setbeamertemplate{headline}
{
  \leavevmode%
  \hbox{%
    \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,right]{section in head/foot}%
      \usebeamerfont{section in head/foot}\insertsectionhead\hspace*{2ex}
    \end{beamercolorbox}%
    \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.65ex,dp=1.5ex,left]{subsection in head/foot}%
      \parbox[b]{.4\textwidth}{
        \usebeamerfont{subsection in head/foot}\hspace*{2ex}\insertsubsectionhead%
        \setcounter{subsectionframenumber}{1}
        \addtocounter{subsectionframenumber}{\insertframenumber}
        \addtocounter{subsectionframenumber}{-\insertsubsectionstartframe}
        \setcounter{totalsubsectionframenumber}{1}
        \addtocounter{totalsubsectionframenumber}{\insertsubsectionendframe}
        \addtocounter{totalsubsectionframenumber}{-\insertsubsectionstartframe}
        \ifnum\thesection>0%
        \foreach\x in {1,...,\thetotalsubsectionframenumber}{%
          \ifnum\x=\thesubsectionframenumber%
          \usebeamertemplate{mini frame}~%
          \else%
          \usebeamertemplate{mini frame in other subsection}~%
          \fi%
        }%
        \fi%
      }%
      %\hfill\hyperlink{toc}{Outline}%
    \end{beamercolorbox}}%
  \vskip0pt%
}


\begin{document}
\begin{frame}[noframenumbering]
  \titlepage
\end{frame}

\begin{frame}[label=toc]
  \frametitle{Outline}
  \tableofcontents
\end{frame}
\section{BLAH}
\subsection{sub1}

\begin{frame}{SLIDE1}\label{slide1}
  \hyperlink{appendix}{\beamergotobutton{More}}
\end{frame}

\begin{frame}{SLIDE2}
\end{frame}

\appendix
\begin{frame}{Extensions}\label{appendix}
  \hyperlink{slide1}{\beamergotobutton{Back}}
\end{frame}

\end{document}