Drawing a node surrounding arbitrarily places nodes

One simple solution is given by Jake in padded boundary of convex hull.

The code:

\documentclass[tikz,border=2bp]{standalone}
\usetikzlibrary{calc,trees}
\newcommand{\convexpath}[2]{
[   
    create hullnodes/.code={
        \global\edef\namelist{#1}
        \foreach [count=\counter] \nodename in \namelist {
            \global\edef\numberofnodes{\counter}
            \node at (\nodename) [draw=none,name=hullnode\counter] {};
        }
        \node at (hullnode\numberofnodes) [name=hullnode0,draw=none] {};
        \pgfmathtruncatemacro\lastnumber{\numberofnodes+1}
        \node at (hullnode1) [name=hullnode\lastnumber,draw=none] {};
    },
    create hullnodes
]
($(hullnode1)!#2!-90:(hullnode0)$)
\foreach [
    evaluate=\currentnode as \previousnode using \currentnode-1,
    evaluate=\currentnode as \nextnode using \currentnode+1
    ] \currentnode in {1,...,\numberofnodes} {
-- ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode)$)
  let \p1 = ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode) - (hullnode\currentnode)$),
    \n1 = {atan2(\y1,\x1)},
    \p2 = ($(hullnode\currentnode)!#2!90:(hullnode\nextnode) - (hullnode\currentnode)$),
    \n2 = {atan2(\y2,\x2)},
    \n{delta} = {-Mod(\n1-\n2,360)}
  in 
    {arc [start angle=\n1, delta angle=\n{delta}, radius=#2]}
}
-- cycle
}

\begin{document}

\begin{tikzpicture}[
    every node/.style={draw,black},
    every path/.style={red},
    scale=2,
    transform shape
]

\node at (0,0) (a) {A}; 
\node at (2,0) (b) {B}; 
\node at (3,0) (c) {C}; 
\node at (2,-1) (e) {E};
\node at (3,-1) (f) {F}; 
 \node at (0,-1) (d) {D}; 

\draw \convexpath{a,b,c,f,e}{12pt};

\end{tikzpicture}
\end{document}

The result:

The problem n. 1 can be addressed by changing the second argument of the \convexpath command.

In case you wonder a smooth alternative, you can proceed as stated in Hobby path realization in convex hull approach. It is, again, something automated:

\documentclass[tikz,border=2bp]{standalone}
\usetikzlibrary{calc,trees,hobby}

\newcommand{\hobbyconvexpath}[2]{
[   
    create hobbyhullnodes/.code={
        \global\edef\namelist{#1}
        \foreach [count=\counter] \nodename in \namelist {
            \global\edef\numberofnodes{\counter}
            \node at (\nodename)
[draw=none,name=hobbyhullnode\counter] {};
        }
        \node at (hobbyhullnode\numberofnodes)
[name=hobbyhullnode0,draw=none] {};
        \pgfmathtruncatemacro\lastnumber{\numberofnodes+1}
        \node at (hobbyhullnode1)
[name=hobbyhullnode\lastnumber,draw=none] {};
    },
    create hobbyhullnodes
]
($(hobbyhullnode1)!#2!-90:(hobbyhullnode0)$)
\pgfextra{
  \gdef\hullpath{}
\foreach [
    evaluate=\currentnode as \previousnode using int(\currentnode-1),
    evaluate=\currentnode as \nextnode using int(\currentnode+1)
    ] \currentnode in {1,...,\numberofnodes} {
    \xdef\hullpath{\hullpath    
  ..($(hobbyhullnode\currentnode)!#2!180:(hobbyhullnode\previousnode)$)
  ..($(hobbyhullnode\nextnode)!0.5!(hobbyhullnode\currentnode)$)}
    \ifx\currentnode\numberofnodes
    \xdef\hullpath{\hullpath .. cycle}
    \else
    \xdef\hullpath{\hullpath
  ..($(hobbyhullnode\nextnode)!#2!-90:(hobbyhullnode\currentnode)$)}
    \fi
}
}
\hullpath
}

\begin{document}

\begin{tikzpicture}[
    every node/.style={black},
    every path/.style={red},
    scale=3,
    transform shape,
    use Hobby shortcut
]

\node at (0,0) (a) {A}; 
\node at (2,0) (b) {B}; 
\node at (3,0) (c) {C}; 
\node at (2,-1) (e) {E};
\node at (3,-1) (f) {F}; 
 \node at (0,-1) (d) {D}; 

\draw \hobbyconvexpath{a,b,c,f,e}{12.5pt};

\end{tikzpicture}
\end{document}

The result: