By default the index starts without a chapter/section-number. If you like the same behaviour than the one for chapters/sections write the following in the preamble.

\renewenvironment{theindex}{%
	\if@twocolumn\@restonecolfalse\else\@restonecoltrue\fi
	\columnseprule \z@
	\columnsep 35\p@
	\twocolumn[\refstepcounter{chapter}%
		\@makechapterhead{\indexname}]%
	\@mkboth{\MakeUppercase\indexname}{\MakeUppercase\indexname}%
	\thispagestyle{plain}\parindent\z@
	\parskip\z@ \@plus .3\p@\relax
	\let\item\@idxitem%
}{%
	\if@restonecol\onecolumn\else\clearpage\fi}

[...]
                \twocolumn[\refstepcounter{section}%
                  \section{\indexname}]%
[...]

Words with leading Umlauts in right order run makeindex with the option -g for a german sorting or use \index{Ubernachtung@Übernachtung} the first is for sorting (without umlaut), the second is the output (the correct word). This method is possible with all words which have special characters.

in latex preamble:

\usepackage{multicol}
\newcommand\NrCol{3}
\renewenvironment{theindex}{%
	\columnseprule \z@
	\columnsep 35\p@
	\section*{\indexname}%
	\@mkboth{\MakeUppercase\indexname}{\MakeUppercase\indexname}%
	\begin{multicols}{\NrCol}%
		\thispagestyle{plain}\parindent\z@
		\parskip\z@ \@plus .3\p@\relax
		\let\item\@idxitem%
}{\clearpage\end{multicols}}

Indexstylefile
makeindex allows to define an own style-file (see man makeindex or /usr/share/doc/makeindex/). if you like an index just like

Symbols
...
A
...
...
B
...
...

then do:

use the stylefile and run manualy:
1. latex myTexFile
2. latex myTexFile
3. makeindex -s PathOfStyleFile/Letter.ist myTexFile
4. latex myTexFile