How to create the following figures in TikZ - Part 2

For (1), it's probably better to define coordinates which do not occupy space, rather than nodes which do occupy space. Loading the calc library will allow you to calculate the coordinate just 1cm above the node (k1):

\coordinate(n1)at($(k1)+(0,1cm)$);

For (2), instead of node[midway,above]{...}, use node[midway,anchor=base,yshift=1ex]{...}. Or, you can group the nodes into one scope and set

\begin{scope}[every node/.append style={anchor=base,yshift=1ex}]
 \draw[latex-latex] (n1) -- (n2) node[midway,] {Text 7};
 \draw[latex-latex] (n2) -- (n3) node[midway,] {Text 8};
 \draw[latex-latex] (n3) -- (n4) node[midway,] {Text 9};
 \draw[latex-latex] (n4) -- (n5) node[midway,] {Text 10};
 \draw[latex-latex] (n5) -- (n6) node[midway,] {Text 11};
\end{scope}

For (3), load the arrows library, add

>=latex

to the tikzpicture options, and pass the option |<->| to \draw (instead of latex-latex):

\draw[|<->|] (n2) -- (n3) node[midway,above] {Text 8};

Full code

\documentclass[tikz,border=5pt]{standalone}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[utf8]{inputenc}
%
\usepackage{tikz}
\usetikzlibrary{matrix,positioning,arrows,calc}


\begin{document}
\begin{tikzpicture}[
kreis/.style={circle,draw,minimum width=20pt},
every node/.style={align=center},
>=latex,
]

\matrix(mat)[row sep=10pt, column sep=60pt] at (0,0) {
\node[kreis](k1) {}; &
\node[kreis](k2) {}; &
\node[kreis](k3) {}; &
\node[kreis](k4) {}; &
\node[kreis](k5) {}; &
\node[kreis](k6) {}; \\    };

 \draw[->] (k1) -- (k2);
 \draw[->] (k2) -- (k3);
 \draw[->] (k3) -- (k4);
 \draw[->] (k4) -- (k5);
 \draw[->] (k5) -- (k6);

\node [below,text width=2.5cm,font=\small] at (k1.south) {Text 1};
\node [below,text width=2.5cm,font=\small] at (k2.south) {Text 2};
\node [below,text width=2.5cm,font=\small] at (k3.south) {Text 3};
\node [below,text width=2.5cm,font=\small] at (k4.south) {Text 4};
\node [below,text width=2.5cm,font=\small] at (k5.south) {Text 5};
\node [below,text width=2.5cm,font=\small] at (k6.south) {Text 6};

\foreach \i in {1,...,6}
\coordinate(n\i)at($(k\i)+(0,1cm)$);

\foreach \j in {1,5,6}
\coordinate(m\j)at($(n\j)+(0,1cm)$);

\foreach \k in {1,6}
\coordinate(k\k)at($(m\k)+(0,1cm)$);


\begin{scope}[every node/.append style={anchor=base,yshift=1ex}]
 \draw[|<->|] (n1) -- (n2) node[midway] {Text 7};
 \draw[|<->|] (n2) -- (n3) node[midway] {Text 8};
 \draw[|<->|] (n3) -- (n4) node[midway] {Text 9};
 \draw[|<->|] (n4) -- (n5) node[midway] {Text 10};
 \draw[|<->|] (n5) -- (n6) node[midway] {Text 11};

 \draw[|<->|] (m1) -- (m5) node[midway] {Text 12};
 \draw[|<->|] (m5) -- (m6) node[midway] {Text 13};

 \draw[|<->|] (k1) -- (k6) node[midway] {Text 14};
\end{scope}
\end{tikzpicture}
\end{document}

With such a regular structure (and once you know how to do it) I think it's easier to create nodes and coordinates with just one matrix. With row #/.style and nodes in empty cells options you can avoid some typing and mix coordinates and kreis nodes. Even text under kreis nodes can be included as nodes' labels. After that, just need to draw arrows between already created reference points.

\documentclass[tikz,border=5pt]{standalone}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[utf8]{inputenc}
%
\usetikzlibrary{matrix,arrows}

\begin{document}

\begin{tikzpicture}[
    kreis/.style={circle,draw,minimum width=20pt},
    every node/.style={align=center},
    >=latex,
]

\matrix(mat)[row sep=7mm, column sep=10pt, matrix of nodes,
             nodes={coordinate},
             row 4/.style={nodes={kreis},
                 every label/.style={rectangle, draw=none, font=\small,
                         text width=2.5cm,align=center}}, 
             nodes in empty cells] 
{
  & & & & & & \\
  & & & & & & \\
  & & & & & & \\[-2mm]    
|[label=below:Text 1]|&
|[label=below:Text 2]|&
|[label=below:Text 3]|&
|[label=below:Text 4]|&
|[label=below:Text 5]|&
|[label=below:Text 6]|\\
};

\foreach \i/\k [count=\j] in {2/Text 7, 3/Text 8, 4/Text 9,
                                    5/Text 10, 6/Text 11}
{
    \draw[->] (mat-4-\j)--(mat-4-\i);
    \draw[|<->|] (mat-3-\j)--(mat-3-\i) node[above,midway]{\k};
}

\draw[|<->|] (mat-2-1) -- (mat-2-5) node[above,midway] {Text 12};
\draw[|<->|] (mat-2-5) -- (mat-2-6) node[above,midway] {Text 13};

\draw[|<->|] (mat-1-1) -- (mat-1-6) node[above,midway] {Text 14};

\end{tikzpicture}
\end{document}

Note:

There is a problem with labels and nodes in TiKZ v2.10. The label node takes node name. This bug has been already solved in cvs version, but a workaround for v2.10 is proposed in Some problems drawing linked lists with TikZ's matrix library. It consists in using name=none in labels options. You can see how it works with:

\matrix(mat)[row sep=7mm, column sep=10pt, matrix of nodes,
             nodes={coordinate},
             row 4/.style={nodes={kreis},
                 every label/.style={rectangle, draw=none, font=\small,
                         text width=2.5cm,align=center}}, 
             nodes in empty cells] 
{
  & & & & & & \\
  & & & & & & \\
  & & & & & & \\[-2mm]    
|[label=below:Text 1]|&
|[label=below:Text 2]|&
|[label=below:Text 3]|&
|[label={[name=none]below:Text 4}]|&
|[label={[name=none]below:Text 5}]|&
|[label={[name=none]below:Text 6}]|\\
};

Edit: now, with version TikZ 3.0.1a the ABOVE code gives expected result: