How can I add Section numbering and a Contents entry to the PDF bookmarks?

Additional bookmarks can be added via \pdfbookmark, see example below. Also I have disabled page anchors for the first pages to avoid duplicate destination names, because some of the pages have the same page number. (Also I have disabled two packages that I do not have installed).

\documentclass[10pt]{article}
\usepackage{graphicx}
\usepackage{epstopdf}
\usepackage{amsmath}
\usepackage{amssymb} 
% \usepackage{fnpct}

\usepackage[a4paper]{geometry}
\geometry{top=1.0in, bottom=1.15in, left=1.15in, right=1.15in}

\usepackage[usenames,dvipsnames]{color}
\usepackage{natbib}
\usepackage[colorlinks=true]{hyperref}
\hypersetup{colorlinks=true, citecolor=ForestGreen, linkcolor=Red,
urlcolor=Blue}

\usepackage{bookmark}
\bookmarksetup{
  numbered, 
  open,
}

% \usepackage{footnotebackref}
\newcounter{intro}
\renewcommand{\theintro}{Int.}


\begin{document}

\hypersetup{pageanchor=false}

\begin{titlepage} \Huge{\sc{Title}} \end{titlepage}

\thispagestyle{empty}
\newpage
\clearpage
\thispagestyle{empty}  
\phantom{a}
\vfill
\newpage
\vfill
\addtocounter{page}{-4}

\begin{center}
\textbf{\Large{Abstract}} \\
\vspace*{0.43 cm}
\noindent This is the abstract so far.
\end{center}

\thispagestyle{empty}
\newpage

\clearpage
\thispagestyle{empty}
\phantom{a}
\vfill
\newpage

\hypersetup{pageanchor=true}
\thispagestyle{empty}
\pdfbookmark[section]{\contentsname}{toc}
\tableofcontents
\newpage


\section*{Introduction}
\addcontentsline{toc}{section}{Introduction}
\refstepcounter{intro}
\label{s:intro}

\section[Title to be added to ToC]{Title to be added to ToC\\
\large Subtitle only appearing in text}\label{label1}
% \large does not take an argument
\subsection{Subsection name here} 
\subsection{Other name here}
\section{Another section}   

\bibliographystyle{plain}
\begin{thebibliography}{99}
...
\end{thebibliography}
\end{document}

As you are using hyperref I dont see the need for any additional package like bookmark For the numbering of regular section : hyperref as has an option bookmarksnumbered which does the job ! For the label of *-section : hyperref also defines a \phantomsectioncommand which creates the expected (unnumbered) bookmark, and which can be used for bookmarking the the toc if you use \addcontentsline{toc}{section}{Contents} to include it in the toc.

Example :

\documentclass[a4paper,11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{hyperref}
\hypersetup{bookmarksnumbered,colorlinks=true}
\begin{document}
\addcontentsline{toc}{section}{Contents}
\phantomsection
\tableofcontents
\clearpage
\section{first}
some text 
\clearpage
\section{second}
another text
\end{document}

where the \clearpage are used only to change the pages of successive sections.

Result :