Q:

The malfunction concerning making sub-section in this Beamer TeX?

In this Beamer TeX, the plane frames are recognized as subsections of the section "Open Questions" such that in the headline there are 5 small circles under the name of the section. Why does that happens? How to correct it?
\documentclass{beamer}
\usetheme{Darmstadt}      

\begin{document}
\section{Open Quetions}
\subsection{Open Questions}
\begin{frame}
\frametitle{Open Questions}
\end{frame}

\begin{frame}[plain]
 \vskip 1cm 
\begin{center}
Thank You!
\end{center}
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\end{document}

A:

There is no malfunction, the plain frames are recognised as frames within the "Open Questions" subsection because they are in this subsection. The plain option just removes the head and footline from these frames, but they are still counted etc. as normal frames.
If you want to switch off the miniframes, you could use How to remove some pages from the navigation bullets in Beamer?
\documentclass{beamer}
\usetheme{Darmstadt}  

\makeatletter
\let\beamer@writeslidentry@miniframeson=\beamer@writeslidentry%
\def\beamer@writeslidentry@miniframesoff{%
  \expandafter\beamer@ifempty\expandafter{\beamer@framestartpage}{}% does not happen normally
  {%else
    % removed \addtocontents commands
    \clearpage\beamer@notesactions%
  }
}
\newcommand*{\miniframeson}{\let\beamer@writeslidentry=\beamer@writeslidentry@miniframeson}
\newcommand*{\miniframesoff}{\let\beamer@writeslidentry=\beamer@writeslidentry@miniframesoff}
\makeatother    

\begin{document}
\section{Open Quetions}
\subsection{Open Questions}
\begin{frame}
\frametitle{Open Questions}
\end{frame}

\miniframesoff

\begin{frame}[plain]
 \vskip 1cm 
\begin{center}
Thank You!
\end{center}
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\miniframeson

\end{document}

You're thank you slide makes me think that maybe you should rather use \appendix:
\documentclass{beamer}
\usetheme{Darmstadt}  

\begin{document}
\section{Open Quetions}
\subsection{Open Questions}
\begin{frame}
\frametitle{Open Questions}
\end{frame}

\appendix

\begin{frame}[plain]
 \vskip 1cm 
\begin{center}
Thank You!
\end{center}
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\begin{frame}[plain]
\end{frame}

\end{document}

