Table headers and chain aligment

Question

I have 2 questions.

1- How to use a diagonal seperator for the table hearders n and k in a good way.

2- How to align the back of the arrow to the rightand the head to the left of the numbers?

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{matrix,chains,scopes,arrows}

\begin{document}
\begin{center}
    \begin{tikzpicture}
      \matrix[matrix of math nodes,column sep=1em,row sep=0ex] (ex5mx) {
        n\backslash{}k & 0 & 1 & 2 \\
        0 & -0.3887696362 & ~ & ~ \\
        1 & -0.3892561049 & -0.3894182612 & ~ \\
        2 & -0.3893777792 & -0.3894183372 & -0.3894183423 \\
      };

      %\draw[thin,black] ([xshift=0em,yshift=0em]ex5mx-1-1.north west) -- ([xshift=0em,yshift=0em]ex5mx-1-1.south east); %\drule
      \draw[thin,black] ([xshift=0.5em,yshift=0em]ex5mx-1-1.north east) |- ([xshift=1.058em,yshift=0em]ex5mx-4-1.south east); %\vrule
      \draw[thin,black] ([xshift=-0.5em,yshift=0.25em]ex5mx-1-1.south west) |- ([xshift=3em,yshift=0em]ex5mx-1-4.south east); %\hrule

      %1st rows
      {[start chain,every on chain/.style={join={by <-*, blue!30}}]
        \chainin (ex5mx-3-3);
        {[start branch] \chainin (ex5mx-2-2); }
        {[start branch] \chainin (ex5mx-3-2); }
      }

      {[start chain,every on chain/.style={join={by <-*, blue!30}}]
        \chainin (ex5mx-4-3);
        {[start branch] \chainin (ex5mx-3-2); }
        {[start branch] \chainin (ex5mx-4-2); }
      }

      %2nd rows
      {[start chain,every on chain/.style={join={by <-*, blue!40}}]
        \chainin (ex5mx-4-4);
        {[start branch] \chainin (ex5mx-3-3); }
        {[start branch] \chainin (ex5mx-4-3); }
      }

    \end{tikzpicture}
    \end{center}
\end{document}