Listing with monospaced font (Dejavu Sans Mono) and background color

Question

I will setup my document to the Sans Serif Font Helvet and additionally all source codes should display with Dejavu Sans Mono and grey background color (on \lstinline{} too). How can I setup listings correctly to do so?

\documentclass[idxtotoc,hyperref,openany,ngerman,11pt]{article} 
\usepackage[a4paper,
            inner=30mm, outer=20mm,
            top=25mm, bottom=25mm,
            headheight=15mm, headsep=7mm
            ]{geometry}

\usepackage{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}
\fontfamily{phv}\selectfont

\usepackage{amsmath,amsfonts,amssymb,amsthm,cancel,icomma,nicefrac,mathrsfs,
            eurosym,verbatim,environ,ifthen,ifdraft,pdfpages,float,booktabs}
\allowdisplaybreaks[1] 

\usepackage{color}
\definecolor{lstgrey}{rgb}{0.95,0.95,0.95}
\usepackage{dejavu}
\usepackage{listings}
\lstset{language=C,
       backgroundcolor=\color{lstgrey},
       frame=single,
       basicstyle=\footnotesize\sf,
       captionpos=b,
       tabsize=2,
  }

\begin{document}
An example listing shows the \lstinline|main()|:

\begin{lstlisting}[caption=main.c]
int main (void)
{
  return 0;
};
\end{lstlisting}

\end{document}

---

Using colorbox and a new command I get the inline listing with a background:

\newcommand\code[1]{\colorbox{lstgrey}{{\lstinline`#1`}}}
...
An example listing shows the \code{main()}:

---

Final code with thanks to AboAmmar:

\documentclass[hyperref,ngerman,11pt]{article} 
\usepackage[a4paper,
            inner=30mm, outer=20mm,
            top=25mm, bottom=25mm,
            headheight=15mm, headsep=7mm
            ]{geometry}

\usepackage{babel}
\usepackage{dejavu}
\usepackage[T1]{fontenc}

\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}

\usepackage{amsmath,amsfonts,amssymb,amsthm,cancel,icomma,
            nicefrac,mathrsfs,eurosym,verbatim,environ,
            ifthen,ifdraft,pdfpages,float,booktabs}
\allowdisplaybreaks[1] 

\usepackage{color}
\definecolor{lstgrey}{rgb}{0.95,0.95,0.95}
\usepackage{listings}
\lstset{language=C,
       backgroundcolor=\color{lstgrey},
       frame=single,
       basicstyle=\footnotesize\ttfamily,
       captionpos=b,
       tabsize=2,
  }
\newcommand\code[1]{\colorbox{lstgrey}{{\lstinline`#1`}}}

\begin{document}
An example listing shows the \code{main()}:

\begin{lstlisting}[caption=main.c]
int main (void)
{
  return 0;
};
\end{lstlisting}

\end{document}

Answer 1

Helvetica for main body and Dejavu Sans Mono for listings, right? OK, observe this line basicstyle=\footnotesize\ttfamily, with that \ttfamily at the end. In your post you used the \sf which was the reason for not getting the Dejavu Sans Mono but still getting Dejavu Sans for every thing. You also issued the command \renewcommand{\familydefault}{\sfdefault} which confirmed this.

\documentclass[hyperref,ngerman,11pt]{article} 
\usepackage[a4paper,
            inner=30mm, outer=20mm,
            top=25mm, bottom=25mm,
            headheight=15mm, headsep=7mm
            ]{geometry}

\usepackage{babel}
\usepackage{dejavu}
\usepackage[T1]{fontenc}

\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}

\usepackage{amsmath,amsfonts,amssymb,amsthm,cancel,icomma,nicefrac,mathrsfs,
            eurosym,verbatim,environ,ifthen,ifdraft,pdfpages,float,booktabs}
\allowdisplaybreaks[1] 

\usepackage{color}
\definecolor{lstgrey}{rgb}{0.95,0.95,0.95}
\usepackage{listings}
\lstset{language=C,
       backgroundcolor=\color{lstgrey},
       frame=single,
       basicstyle=\footnotesize\ttfamily,
       captionpos=b,
       tabsize=2,
  }

\begin{document}
An example listing shows the \lstinline|main()|:

\begin{lstlisting}[caption=main.c]
int main (void)
{
  return 0;
};
\end{lstlisting}

\end{document}