I don't think you need a new class here; you can use one of the standard classes (article
, for example) and define your environment and commands with the help of some packages.
Here's one possibility using the tcolorbox
package to define some framed boxes for the speakers (the partner and you); the conversation
environment and the \partner
and \me
commands act as requested:
\documentclass{article}
\usepackage[a5paper]{geometry}% paper size just for the example
\usepackage[dvipsnames]{xcolor}
\usepackage{tcolorbox}
\usepackage{lipsum}% just to generate text for the example
\tcbuselibrary{most}
\newcommand\cpartner{}
\newenvironment{conversation}[3]
{\clearpage%
\noindent\parbox{\linewidth}{%
\gdef\cpartner{#1}%
\centering
{\Large\textsc{#1}}\par{\large\texttt{#2}\par#3\par}}%
\par\nobreak
}
{\par\bigskip}
\newtcolorbox{partn}[1][]{%
breakable,
enhanced,
colback=white,
title=\parbox{\linewidth}{\cpartner\par#1},
coltitle=black,
colframe=MidnightBlue!60,
colbacktitle=MidnightBlue!20,
before=\vskip20pt\noindent
}
\newtcolorbox{mebox}[1]{%
breakable,
enhanced,
colback=white,
title=Reply on #1,
coltitle=black,
colframe=Maroon!50,
colbacktitle=Maroon!20,
}
\newcommand\partner[2][]{%
\begin{partn}[#1]#2\end{partn}}
\newcommand\me[2]{%
\begin{mebox}{#1}#2\end{mebox}}
\begin{document}
\begin{conversation}{Kate Johnson}{kjohnson@gmail.com}{Birthday party}
\partner[28 August 1999]{\lipsum[2]\lipsum[4]}
\me{29 August 1999}{\lipsum[4]}
\partner[31 August 1999]{\lipsum[4]}
\me{2 September 1999}{\lipsum[4]}
\end{conversation}
\begin{conversation}{Liz Taylor}{ltaylor@gmail.com}{Resignation}
\partner[28 August 1999]{Some short message}
\me{29 August 1999}{A reply}
\partner[31 August 1999]{Some short message}
\me{2 September 1999}{A reply}
\end{conversation}
\end{document}

Another, more sober, alternative. In this approach, a List of all Conversations (similar to a table of contents) will be automatically produced; each entry will have the name of the partner and the topic of the conversation; colors different from black were suppressed:
\documentclass{article}
\usepackage[a5paper]{geometry}
\usepackage[dvipsnames]{xcolor}
\usepackage{tcolorbox}
\usepackage[explicit]{titlesec}
\usepackage{titletoc}
\usepackage{lipsum}
\tcbuselibrary{most}
\renewcommand\thesection{}
\titleformat{\section}
{\normalfont\Large\centering}{}{0em}{#1}
\newcommand\sectionbreak{\clearpage}
\newcommand\cpartner{}
\newenvironment{conversation}[3]
{\gdef\cpartner{#1}%
\section[\textsc{#1}~(#3)]{\textsc{#1}\\\texttt{#2}\\#3}
}
{\par}
\newtcolorbox{partn}[1][]{%
breakable,
enhanced,
colback=white,
arc=0pt,
outer arc=0pt,
title=\parbox{\linewidth}{\cpartner\par#1},
coltitle=black,
colframe=black,
boxrule=0.8pt,
colbacktitle=white,
before=\vskip20pt\noindent
}
\newtcolorbox{mebox}[1]{%
breakable,
enhanced,
arc=0pt,
outer arc=0pt,
colback=white,
title=Reply on #1,
coltitle=black,
colframe=black,
boxrule=0.8pt,
colbacktitle=white,
}
\newcommand\partner[2][]{%
\begin{partn}[#1]#2\end{partn}}
\newcommand\me[2]{%
\begin{mebox}{#1}#2\end{mebox}}
\renewcommand\contentsname{Conversations}
\titlecontents{section}[0em]
{}
{\contentslabel{0em}}
{}
{\titlerule*[1000pc]{.}\contentspage}
\begin{document}
\tableofcontents
\begin{conversation}{Kate Johnson}{kjohnson@gmail.com}{Birthday party}
\partner[28 August 1999]{\lipsum[2]}
\me{29 August 1999}{\lipsum[2-3]}
\partner[31 August 1999]{\lipsum[4]}
\me{2 September 1999}{\lipsum[4]}
\end{conversation}
\begin{conversation}{Liz Taylor}{ltaylor@gmail.com}{Resignation}
\partner[28 August 1999]{Some short message}
\me{29 August 1999}{A reply}
\partner[31 August 1999]{Some short message}
\me{2 September 1999}{A reply}
\end{conversation}
\begin{conversation}{Marcus Rump}{mrump@gmail.com}{Interesting offer}
\partner[28 August 1999]{Some short message}
\me{29 August 1999}{A reply}
\partner[31 August 1999]{Some short message}
\me{2 September 1999}{A reply}
\end{conversation}
\end{document}
