Maybe you are more satisfied with the following layout:
\documentclass[11pt,a4paper,numbers=noenddot]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[left=2cm, right=1cm]{geometry}
\usepackage{paracol}
\setcolumnwidth{3.5cm,9.1cm,5cm}
\setlength{\columnsep}{0.2cm}
\usepackage{lipsum}
\usepackage[bookmarks=false]{hyperref}
\begin{document}
\begin{paracol}{3}[\section{\underline{SECTION I - The Project Statement}}]
\switchcolumn[0]
\subsection{Subsection 1}\label{subsec:first}
\switchcolumn[1]
\sloppy
\lipsum[1]
\switchcolumn[2] {\raggedright
see \texttt{www.example.com/example}}
\switchcolumn[1]*
\sloppy
\lipsum[2]
\switchcolumn[2]{\raggedright
see \texttt{Mayer et. al.} }
\switchcolumn[0]*
\subsection{A longer Subsection with a quite long title}
\switchcolumn[1]
\sloppy
\lipsum[4]
\switchcolumn[2]{\raggedright
\texttt{As already shown in \autoref{subsec:first}}}
\switchcolumn[0]*
\subsubsection{heading of a subsubsection}
\end{paracol}
\end{document}
What I changed in comparison to your original layout: I used a larger width for the first and third column and also explicitly specified the width between the columns.
Why did I decide to change the above mentioned values? Let's have a look at the following MWE that is essentially a shortened version of your code where I have just added some code to generate colored lines. The red lines indicate the textwidth and the blue lines indicate the widths of the columns you chose.
\documentclass[11pt,a4paper,numbers=noenddot]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[left=2cm, right=1cm]{geometry}
\usepackage{paracol}
\setcolumnwidth{10pt,60pt,10pt}
%%%% Colored lines %%%%
\usepackage{showframe}
\renewcommand*\ShowFrameColor{\color{red}}
\setlength{\columnseprule}{0.4pt}
\colseprulecolor{blue}
%%%% %%%%
\usepackage{lipsum}
\begin{document}
\begin{paracol}{3}[\section{\underline{SECTION I - The Project Statement}}]
\switchcolumn[0]
\subsection{Subsection1}
\switchcolumn[1]
\sloppy
\lipsum[1]
\switchcolumn[2]
see \texttt{www.example.com/example}
\end{paracol}
\end{document}
As you can see from the above example, your left column is too narrow for the text it contains. Only the quite large standard width between columns (\columnsep) prevents the subsection header from overlapping with the text in the middle column. Also the widths of your columns added up are wider than the textwidth:
left col + columnsep + middle col + columnsep + right col > textwidth
To overcome this issue I have recalculated the widths as follows: A standard A4 paper is 21 cm wide. If we substract the left and right margin (2 and 1 cm respectively) that you have set via geometry, we end up with a textwidth of 18 cm that we can use for the column. These 18 cm are split up into three columns as follows with 0.2 cm being the width of the white space between the columns.
3.5 cm + 0.2 cm + 9.1 cm + 0.2 cm + 5 cm = 18 cm
If we now add the following block of code into the first MWE, we obtain the following result. From this, we can clearly see that now the columns don't overlap with each other or the margins.
\usepackage{showframe}
\renewcommand*\ShowFrameColor{\color{red}}
\setlength{\columnseprule}{0.4pt}
\colseprulecolor{blue}
\subsection, should the headings stay inside the left column or can they stick into the main column if they are wider? Is the right column height aligned to the contents the remarks are about or filled from the top? – Skillmon Jun 23 '19 at 13:37\autorefcommand. Writing my answer, I did not encounter any problems with this command. Could you please add some information regarding your use of\autoref, please? – leandriis Jun 23 '19 at 14:24