How to draw on a tikz picture without shifting it

The tikzpicture shifts because tikz computes the bounding box from all coordinates mentioned in the picture. This includes the labels that protrude from the image.

Include the line

\useasboundingbox (image.south east) rectangle (image.north west);

after defining the node image. This tells tikz to use this rectangle as bounding box instead of computing the box itself.

18cm is a bit large for the image. But beside this: you can use a scope with overlay:

\documentclass{article}

\usepackage{graphicx}
\usepackage{rotating}
\usepackage{subfigure}
\usepackage{tikz}
\usepackage{tikz-imagelabels}
\usepackage{caption}
\usetikzlibrary{arrows,snakes,backgrounds}


\begin{document}

\begin{figure}
\centering
\begin{tikzpicture}\node[anchor=south west,inner sep=0] (image) at (0,0){\includegraphics[width=18cm]{example-image}};
\begin{scope}[x={(image.south east)},y={(image.north west)}]

        \draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1);
      \foreach \x in {0,1,...,9} { \node [anchor=north] at (\x/10,0) {0.\x}; }
        \foreach \y in {0,1,...,9} { \node [anchor=east] at (0,\y/10) {0.\y}; }

    \begin{scope}[overlay] %<----
     \draw [thick, ->] (-0.05, 0.57) -- (0.07, 0.57);
     \filldraw [thick] (-0.18, 0.57)  node[anchor=west] {Kühlkanäle};

    %
     \draw [thick, ->] (-0.05, 0.8) -- (0.2, 0.63);
     \filldraw [thick] (-0.25, 0.8)  node[anchor=west] {Stirnseitiger Reibring};

    %
     \draw [thick, ->] (-0.05, 0.4) -- (0.2, 0.4);
     \filldraw [thick] (-0.25, 0.8)  node[anchor=west] {Stirnseitiger Reibring};
    \end{scope} %<--------
    \end{scope}
\end{tikzpicture}
\end{figure}


\end{document}