To answer the specific question:
A label can be coloured with the same syntax you used for shift
ing the A and B labels, only by writing the colour name in the brackets, e.g.
\coordinate [label={[blue]left:$D$}] (D) at (0.3,0.5);
If you want to set the colour of all labels in a picture, use the every label
style, e.g.
\begin{tikzpicture}[every label/.style={color=blue}]
...
You don't need anything but basic TikZ for that.
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=2]
\draw[->] (0,0,0) -- (3,0,0) node[below]{$x_1$};
\draw[->] (0,0,0) -- (0,0,3) node[below]{$x_2$};
\draw[->] (0,0,0) -- (0,3,0) node[left]{$x_3$};
\node[circle,draw,fill=black,label=below:$T_1$,scale=0.7] (b1) at (0,0,2){};
\node[circle,draw,fill=black,label=below:$T_2$,scale=0.7] (b2) at (2,0,0){};
\node[circle,draw,fill=black,label=right:$T_2$,scale=0.7] (b3) at (0,2,0){};
\draw[thick,-] (b1) -- node[midway,below,sloped]{$g$ (Schnittgerade)} (b2) -- (b3) -- (b1);
\fill[blue,opacity=0.2] (2,0,0) -- (0,0,2) -- (0,3,2) -- (2,3,0) -- node[midway,right]{$E$} cycle;
\end{tikzpicture}
\end{document}
Best Answer
after some hours and following your tips I've arrived at a acceptable solution.
Result: