biblatex: excluding shorthand entries from the main bibliography

Your style modifications are unrelated to your actual problems. :-) That said, here's how to solve them:

1. To exclude entries with a shorthand field from the "normal" bibliography, define a corresponding bibcheck. See section 3.5.9 of the biblatex manual for details.

2. To typeset the bibliography and the list of shorthands as \section* instead of \chapter* in the book/report class, use the "subbibliography" heading and a custom-defined "subshorthands" heading. See section 3.5.7 of the manual for details.

---

\documentclass{book}

\usepackage[style=verbose]{biblatex}

\defbibcheck{noshorthand}{%
  \iffieldundef{shorthand}{}{\skipentry}%
}

\makeatletter
  \defbibheading{subshorthands}[\losname]{%
    \section*{#1}%
    \if@twoside\markright{\MakeUppercase{#1}}\fi}
\makeatother

\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@misc{A01,
  shorthand = {Aut},
  author = {Author, A.},
  year = {2001},
  title = {Alpha},
}
@misc{B02,
  author = {Buthor, B.},
  year = {2002},
  title = {Bravo},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\nocite{*}

\begin{document}

\printbibheading

\printshorthands[heading=subshorthands]

\printbibliography[heading=subbibliography,title={Other References},check=noshorthand]

\end{document}