Tikz problems, arrowhead touches line, shadow influence

Question

I have three problems with a tikz picture given in the MWE below.

The first problem is that the head of the arrow lies on the line/border of the Brectangle (not much, but some visible pixels). What I would like to achieve is that the head of the arrow ends directly at the line.

The second problem occurs where the line/border of the A rectangle crosses the shadow of the B rectangle. The part which lies under the shadow is gray which is correct. However, I would like to have the line "above" the shadow and thus no influence on its color appearance.

The last problem occurs where the line/border of the A rectangle crosses the dashed line/border of the E rectangle. Here the line of A should end at the border of the dashed line and not in the middle of it.

Edit: Pictures added

First problem:

Second problem:

Third problem:

MWE

\documentclass {report} 


\usepackage{tikz}
\usetikzlibrary{arrows,arrows.meta,positioning}
\usetikzlibrary{shadows}

\begin{document}


\begin{tikzpicture}
[
    box/.style ={draw,minimum height=0.9cm,minimum width=2.1cm,inner sep=4,align=center,fill=white,drop shadow={opacity=0.4,shadow xshift=.3ex,shadow yshift=-.3ex}},
    arrowstyle/.style={-{Latex[angle=90:8pt]},line width=4pt, rounded corners=10pt}
]


    \node[draw,minimum width=4cm,minimum height=1.4cm](D){};
        \node[right=0.5cm of D.west](A){A};
        \node[box, above right = 0.4cm and -1.5cm of A.east](B){B};
        \node[box, above = 2cm of B.north](C){C};

        \node[draw,minimum height=2.2cm,minimum width=3cm,thick,dashed,align=center,fill=white,right = 1.3cm of B.east](E){E};

    \draw[->,arrowstyle,gray!90]    (C.south) -- (B.north); 

\end{tikzpicture}


\end{document}

Answer 1

1. Fixed by shorten >=.1pt.

2. Fixed by drawing the rectangle of node D afterwards, over the gray shadowed area. Clipping is needed for preventing drawing inside nodes B and E.

3. Fixed by Clipping.

Full example:

\documentclass {report}

\usepackage{tikz}
\usetikzlibrary{arrows,arrows.meta,positioning}
\usetikzlibrary{calc}
\usetikzlibrary{shadows}

\begin{document}


\begin{tikzpicture}[
  box/.style ={
    draw,
    minimum height=0.9cm,
    minimum width=2.1cm,
    inner sep=4,
    align=center,
    fill=white,
    drop shadow={
      opacity=0.4,
      shadow xshift=.3ex,
      shadow yshift=-.3ex,
    },
  },
  arrowstyle/.style={
    -{Latex[angle=90:8pt]},
    line width=4pt,
    rounded corners=10pt,
  },
]

  \node[
    % draw,
    minimum width=4cm,
    minimum height=1.4cm,
  ] (D) {};
  \node[right=0.5cm of D.west](A){A};
  \node[box, above right = 0.4cm and -1.5cm of A.east](B){B};
  \node[box, above = 2cm of B.north](C){C};

  \node[
    draw,
    minimum height=2.2cm,
    minimum width=3cm,
    thick,
    dashed,
    align=center,
    fill=white,
    right = 1.3cm of B.east,
  ] (E) {E};

  \draw[->, arrowstyle, gray!90, shorten >=.1pt] (C.south) -- (B.north);

  \begin{scope}
    \clip (B.south west) -- (B.south east) -- (B.north east)
      -- (E.north west) -- (E.south west) -- (E.south east)
      -- ($(current bounding box.south east) + (0pt, -.4pt)$)
      -- (current bounding box.south west) -- cycle
    ;
    \draw (D.south west) rectangle (D.north east);
  \end{scope}

\end{tikzpicture}
\end{document}