Latex article: unable remove the titles of table of contents, list of figures, list of tables - \contentsname{} doesn't work

Question

I need an article with specific formatting, which I almost got. The problem is that I am not able to delete the default titles of table of contents, list of figures, list of tables and I do not understand why. I post the code:

\documentclass[13,titlepage]{article}
%\usepackage[utf8]{inputenc}
\usepackage[a4paper,
            left=4cm,
            right=1.5cm,
            top=3cm,
            bottom=3.5cm]{geometry}
\usepackage{ifxetex,ifluatex}
\ifluatex
  \usepackage{unicode-math}
  \setmainfont{Times New Roman} % text font
  \setmathfont{XITS Math} % Times Roman math font
\else\ifxetex
  \usepackage{fontspec}
  \setmainfont{Times New Roman}
  % possibly need to choose a suitable math font
\else
  \usepackage[T1]{fontenc}
  \usepackage[utf8]{inputenc}
  \usepackage{newtxtext,newtxmath}
\fi\fi
\usepackage{amsmath}
\usepackage{lipsum}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage{xcolor}
\usepackage{sectsty} % use 20% "leading"
\sectionfont{\fontsize{13}{1.25}\selectfont}
\subsectionfont{\fontsize{13}{1.25}\selectfont}
\usepackage{cite}
\linespread{1.25}
\usepackage[fontsize=13pt]{scrextend}
\usepackage[affil-it]{authblk} 
\usepackage{etoolbox}
\usepackage{lmodern}
\usepackage{tocloft}
\renewcommand\Authfont{\fontsize{13}{14.4}\selectfont}
\renewcommand\Affilfont{\fontsize{13}{10.8}\itshape}
\usepackage{graphicx}
\usepackage{array}
\graphicspath{ {figures/} }
\renewcommand{\contentsname}{}
\renewcommand{\cftsecleader}{\cftdotfill{\cftdotsep}}
\renewcommand{\listfigurename}{}
\renewcommand{\listtablename}{}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@book{xxxxx1974values,
  title={Values xxxxx},
  author={Xxx, Xxx X.},
  year={1974},
  publisher={Princeton University Press}
}
\end{filecontents*}
\usepackage[backend=biber,style=apa]{biblatex}
\addbibresource{\jobname.bib}
\renewcommand{\thepage}{\Roman{page}}
\title{Title}
\author{Author}
\date{Date}
\begin{document}
\maketitle
\setcounter{page}{2}
\newpage
\section*{Table of Contents}
\begingroup
\let\clearpage\relax
\vspace{-1.25cm} % the removed space. Set as appropriate
\tableofcontents
\endgroup
\newpage
\section*{List of Figures}
\listoffigures
\newpage
\section*{List of Tables}
\listoftables
\newpage
\section*{List of Abbreviations}
\begin{tabular}{ll}
\end{tabular}
\newpage
\section{Section 1}
\thispagestyle{plain}
\renewcommand{\thepage}{\pagenumbering{arabic}}
Xx
\section{Section 2}
\subsection{Xx}
Xx
\subsection{Xx}
Xx
\end{document}

Answer 1

As one can see in this answer you have to use

\addto\captionsamerican{%
   \renewcommand{\contentsname}{}%
}

below loading babel instead of renewing \contentsname.