Generating chapter title

Question

I am trying to prepare chapters in my thesis as par the following requirements

1. Chapter number (in Arabic) shall appear as right justified at the top of the page in Candara 27 pt in italic face, and title using first letter capitals. No vertical gap shall be left between Chapter number and Chapter title. A gap of 5 lines (of 11pt thickness) should be used between Chapter heading and first paragraph.

2. A chapter can be divided into Sections, Sub­sections, and Sub-subsections so as to present different concepts separately. Sections and sub­sections can be numbered using decimal, e.g., 2.2 for the second section in Chapter 2 and 2.3.4 for the fourth sub­section in the third Section of Chapter 2. The Sub-subsections shall be numbered as “(a)”, “(b)”, ... No further sub-sectioning shall be done beyond this third level. Chapters, Sections, and Sub­sections shall be included in the contents with page numbers flushed to the right; the inner subsections shall not be included in the contents.

3. Chapter number should be started from 1.

I have prepared a main.tex file where I am including all my chapters one by one. A part of my code is as follows:

\documentclass[twoside, 11pt]{book}
\usepackage[top = 1.25cm, bottom = 1.25cm, left = 3.5cm, right = 1.25cm]{geometry}
\pagestyle{plain}
\usepackage{palatino, amsmath, amssymb, amsthm, bookmark}
\usepackage{graphicx}
\graphicspath{{figures/}}

\begin{document}

\frontmatter
    \include{frontpage/frontpage}

\tableofcontents
\include{toc}

\pagenumbering{arabic}\setcounter{page}{1}

\mainmatter
    \include{chapter2/chapter2}

\backmatter
\pagenumbering{roman}\setcounter{page}{1}
\bibliographystyle{plain}
\bibliography{library}
\end{document} 

Chapter 2 begins with:

\chapter{Review of Literature} 

\section{Preliminaries of Graph theory}

    A graph $G = (V(G), E(G))$ is a

I am facing the following problems.

1. It does not generate the chapter number above the title.

2. Chapter numbering starts with 0.

Can you help me to fix them accordingly?

Answer 1

Here is a first draft. I had to replace Candara by another font, as there's no package to use it with pdflatex (however, it can be used with fontspec and xe/lualatex):

\documentclass[twoside, 11pt]{book}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[vmargin= 1.25cm, left = 3.5cm, right = 1.25cm, showframe]{geometry}
\usepackage{titlecaps}
\setcounter{secnumdepth} {3}
\pagestyle{plain}
\usepackage{amsmath, amsthm, bookmark}%
\usepackage{newpxtext, newpxmath}
\usepackage{graphicx}
\graphicspath{{figures/}}
%
\usepackage[explicit]{titlesec} 
\usepackage{titletoc}
\titleformat{\chapter}[block]{\fontfamily{verdana}\fontsize{27pt}{34pt}\selectfont\filleft}{\thechapter.}{0.5em}{#1}
\titleformat{name=\chapter, numberless}[block]{\fontfamily{verdana}\fontsize{27pt}{34pt}\selectfont\filleft}{}{0em}{#1}
\titlespacing{\chapter}{0pt}{12pt plus 2pt minus 2pt}{36pt}

\titleformat{\section}{\fontfamily{verdana}\Large}{\thesection}{0.5em}{#1}
\titleformat{name=\section, numberless}{\fontfamily{verdana}\Large}{}{0em}{\addcontentsline{toc}{section}{#1}#1}

\titleformat{\subsection}{\fontfamily{verdana}\large}{\thesubsection}{0.5em}{#1}
 \titleformat{name=\subsection, numberless}{\fontfamily{verdana}\large}{}{0em}{\addcontentsline{toc}{subsection}{#1}#1}

 \titleformat{\subsubsection}{\fontfamily{verdana}\large}{\thesubsubsection}{0.5em}{#1}
\renewcommand\thesubsubsection{(\alph{subsubsection})}

\titlecontents{chapter} [0em] %
{\bigskip\fontfamily{verdana}\selectfont \bfseries}
{\thecontentslabel\quad}%\thecontentslabel
{}% numberless
{\hfill\contentspage}[\smallskip] %

\titlecontents{section} [1.667em] %
{\medskip\fontfamily{verdana}\selectfont}
{\thecontentslabel\enspace}%\thecontentslabel
{\hspace*{2.12em}}%numberless
{\titlerule*[1pc]{.}\contentspage}[\smallskip]%

\titlecontents{subsection} [3.76em] %
{\medskip\fontfamily{verdana}\selectfont}
{\thecontentslabel\enspace}%\thecontentslabel
{\hspace*{3.12em}}%numberless
{\titlerule*[1pc]{.}\contentspage}[\smallskip]%

\begin{document}

\tableofcontents

\chapter{Review of Literature}

\section{Preliminaries of Graph theory}

    A graph $G = (V(G), E(G))$ is a

\section*{An unnumbered section}

\subsection{Different Kinds of Graphs}

\subsection*{Other Kinds of Graphs}

\subsubsection{A test subsub}

\end{document}