Add "Appendix" before "A" for Appendix A in thesis TOC

Add the following to your preamble:

\usepackage[titletoc]{appendix}
\makeatletter
\renewcommand\backmatter{
    \def\chaptermark##1{\markboth{%
        \ifnum  \c@secnumdepth > \m@ne  \@chapapp\ \thechapter:  \fi  ##1}{%
        \ifnum  \c@secnumdepth > \m@ne  \@chapapp\ \thechapter:  \fi  ##1}}%
    \def\sectionmark##1{\relax}}
\makeatother

The appendix package adds some extra functionality for dealing with appendices. This extra functionality (including the one you need) is accessed by using the \appendices environment instead of the \appendix command. So changing your thesis class \backmatter command to remove the \appendix command, along the with [titletoc] option of the package (which appends the appendix name to the letter in the TOC) should solve your problem.

Now in your actual thesis tex file you should do the following:

\backmatter
\begin{appendices}
\chapter{An appendix}
...
\end{appendices}
\bibliography{}