tikz curve normal vector

Question

I'm trying to do a nice sketch using tikz.

My tikz code is like this:

\documentclass[]{scrartcl}  
\usepackage{tikz}   
\usetikzlibrary{arrows}       
\begin{document}

\begin{tikzpicture}[allow upside down, scale=1]
%(0,0)(0.70,1.9)(1.41,3.6)
%\draw plot [smooth, tension=0.5] coordinates{(2.13,5.1)(2.86,6.4)(3.62,7.5)(4.42,8.4)(5.30,9.1)(6.34,9.6)(7.13,9.8)(8.42,9.9)}
\draw[red,line width=1pt] (2.13,5.1) -- (2.86,6.4) -- (3.62,7.5) -- (4.42,8.4) -- (5.30,9.1) -- (6.34,9.6) -- (7.13,9.8) -- (8.42,9.9) [smooth, tension=0.5]
node[sloped,inner sep=0cm,above,pos=.5,
anchor=south west,
minimum height=2cm,minimum width=1cm](N){};

\path (N.south west)
edge[->,blue] node[left] {$\vec{ n}$} (N.north west);

\end{tikzpicture}

\end{document}

Mostly taken from there: How to draw tangent vectors and component vectors on a curve My Problems:

1. How do I define the point for the normal vector?
2. I'd really like that smooth ... how?
3. How do I add another vector (same target, but other angle)

Output of the current code:

What I'm trying to do:

Answer 1

1. You have to put the node at appropriate places:

   \draw[red,line width=1pt,smooth, tension=1.9,samples=1000] (2.13,5.1) -- 
   node[sloped,inner sep=0cm,above,pos=.5, anchor=south west,
   minimum height=2cm,minimum width=1cm](N){}(2.86,6.4) -- (3.62,7.5) -- (4.42,8.4) --
   (5.30,9.1) -- (6.34,9.6) -- (7.13,9.8) -- (8.42,9.9)node[black,above,anchor=west] 
   {Frontwant};
   

2. You can use rounded corners=<dimension>. Choose proper <dimension>.

3. Using calc library, add x value to (N.east). Reverse the arrow direction:

    \path  (N.south west) edge[stealth-,red!50!black,shorten <=2pt]   ($(N.east) + 
    (0.3,0)$) node[above=1.4cm] {$\hat{S}$};
   

   Change 0.3 in ($(N.east) + (0.3,0)$) to suit the angle you want.

With all the above, and lot of additions, the full code:

\documentclass[]{scrartcl}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,positioning}
\begin{document}

\begin{tikzpicture}[allow upside down, scale=1]
%(0,0)(0.70,1.9)(1.41,3.6)
%\draw plot [smooth, tension=0.5] coordinates{(2.13,5.1)(2.86,6.4)(3.62,7.5)(4.42,8.4)(5.30,9.1)(6.34,9.6)(7.13,9.8)(8.42,9.9)}
\draw [red,line width=1pt,smooth, tension=1.9,samples=1000,rounded corners=15pt] (2.13,5.1) -- node[sloped,inner sep=0cm,above,pos=.5,
anchor=south west,
minimum height=1cm,minimum width=0.5cm](N){}(2.86,6.4) -- (3.62,7.5) -- (4.42,8.4) --  (5.30,9.1) -- (6.34,9.6) -- (7.13,9.8) -- (8.42,9.9)node[black,above,anchor=west] {Frontwand}
;

%% vectors
\path (N.south west)
edge[-stealth,blue] node[below,pos=0.9] {$\vec{ n}$} (N.north west);
\path  (N.south west) edge[stealth-,red!50!black,shorten <=2pt] node[above,pos=1,text=red!50!black] {$\hat{S}$  }   ($(N.east) + (0,0.5)$);
%% horizontal lines and coordinates...
\path[draw,red!70!green] ($(N.south west) + (-2,0)$) -- ($(N.south west) + (7,0)$)node[coordinate, pos=0] (a){} node[coordinate,pos=1,label=right:{\color{black}$z$}] (b){} node[pos=.3,above=-0.1cm,black] {$A(z)$};
\path[draw,red!70!green] (a |- 2.86,6.4 ) -- (b |- 2.86,6.4)node[pos=1,anchor=west,black](c) {$z-1$}node[pos=.38,above=-0.1cm,black] {$A(z-1)$};
%% Co ordinate system
\node [right=1.5cm of b,scale=0.9] (O) {$\bigotimes$};
\draw[-latex](O.center) -- (c -| O)node[above]{$z$};
\draw[-latex](O.center) -- +(0:.7cm)node[right]{$x$};
\draw[-latex,shorten >= -5pt] (O.center) -- (O.north east) node[pos=1.8]{$y$};
\fill (N.south west) circle (2pt);
\fill (2.86,6.4) circle (2pt);

\end{tikzpicture}

\end{document}

While I did not optimize the code, lot of typing could have been saved. I left it more verbose.

Answer 2

Another attempt where the first 4 coordinates of OP are borrowed.

Code:

\documentclass[]{article}  
\usepackage{tikz}   
\usetikzlibrary{arrows,positioning}       
\begin{document}

\begin{tikzpicture}[scale=1.5]
\draw[black,thick] (-1,6.4)--(5,6.4) node[right]{$z-1$};
\draw[black,thick] (-1,5.1)--(5,5.1) node[right]{$z$};
\draw[black,thick,->] (7,5.5) node[label=below:$y$]{$\bigotimes$}-- (8,5.5)node[right]{$x$}; 
\draw[black,thick,->] (7,5.5) -- (7,6.5)node[right]{$z$}; 
\draw[black, line width=2pt] (1.7,4.1) -- (2.13,5.1) node[above right,xshift=5pt]{$A(z)$} -- (2.86,6.4) node[above right,xshift=5pt]{$A(z-1)$} -- (3.62,7.5) -- (4.42,8.4) node[above right]{Frontwand};
\draw[->,>=stealth',thick] (2.13,5.1) -- +(120:0.8cm) node[above left]{$n$};
\node[fill=black, circle, scale=0.5,pin={[pin distance=2cm,pin edge={<-,>=stealth'}]above:{$\hat S$}}] at  (2.13,5.1){};
\node[fill=black, circle, scale=0.5] at (2.86,6.4){};
\end{tikzpicture}

\end{document}