\documentclass[a4paper,fontsize=12pt,listof=totoc,toc=sectionentrywithdots]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{emoji}
\setemojifont{NotoColorEmoji}
\usepackage{polyglossia}
\setdefaultlanguage{german}
\usepackage{lmodern}
\usepackage[onehalfspacing]{setspace}
\setcounter{secnumdepth}{5} % numbered paragraphs
\usepackage{fancyhdr}
    \setlength{\headheight}{15.2pt}
    \pagestyle{fancy}
    \fancyhf{}
    \fancyhead[R]{\Autor}
    \fancyhead[L]{\Hausaufgabe}
    \fancyfoot[C]{\thepage}

%
% math packages
%

\usepackage{mathtools}
\usepackage{amsxtra,amssymb,amsthm,amstext,amsfonts}
\usepackage{esint} % for circle integrals

%
% microtype setting
%

\usepackage{float} % better control of placements
\usepackage{microtype} % package for optimising typographic details

%
% tables
%

\usepackage{booktabs} % optimised display of tables
\usepackage{tabularx} % more modern display of tables with \toprule,\midrule,\bottomrule
\usepackage{multirow} % allows table cells over multiple rows within a column

%
% misc packages
%

\usepackage[extendedchars]{grffile} % for spaces and special chars in file paths
\usepackage{xcolor} % adds colours
\usepackage{multicol} % allows dividing (parts of) the page into multiple columns
\usepackage[hyphens]{url} % adds hyperlinks
\usepackage[]{hyperref} % adds links to toc

%
% custom commands
%
\newcommand{\Hausaufgabe}{Modulname - Hausaufgabe Nr. X} % title, for both title and header
\newcommand{\Aufgabe}[1]{ \section*{#1.)} \addcontentsline{toc}{section}{Aufgabe #1} \label{sec:aufgabe_#1}}
\newcommand{\Teilaufgabe}[1]{ \subsection*{#1)} \addcontentsline{toc}{subsection}{#1 )}}
\newcommand{\Autor}{Max Mustermann} % your name here

%
% math related custom commands
%

\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\phi}{\varphi}
\newtheorem{lemma}{Lemma}

%
% maketitle
%

\title{\Hausaufgabe}
\author{\Autor}
\date{\today}

%
% document
%

\begin{document}
\maketitle
\tableofcontents

\Aufgabe{1}
\Teilaufgabe{a}
Beispiel

\end{document}