Tikz: Draw Rectangle around a rotated non-regular shape

Question

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture}
\begin{scope}[rotate=-{30}]
\draw (0,0)--(0,4)--(4,4)--(4,2)--(6,2)--(6,0)--(4,0)--(4,-2)--(2,-2)--(2,0)--cycle;
\draw (2, 0)--++(2,0);
\draw (0, 2)--++(4,0);
\draw (2,4)--++(0,-4);
\draw (4,2)--++(0,-2);
\end{scope}
\end{tikzpicture}
\end{document}

1. What is the proper way to draw a rectangle around this shape so that it touches far left, right, top, bottom points?
2. I have a feeling that I haven't constructed the non-regular shape in a systematic manner. How could I do it better?
3. [Addendum upon Torbjørn's initial answer] How can I fill the bounding box, but exclude the shape inside? And how can I, say, draw a line from the shape to the bounding box.)

Answer 1

An easy way is to use the fit library along with a local bounding box.

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{fit}
\begin{document}
\begin{tikzpicture}
\begin{scope}[rotate=-{30},local bounding box=a]
\draw (0,0)--(0,4)--(4,4)--(4,2)--(6,2)--(6,0)--(4,0)--(4,-2)--(2,-2)--(2,0)--cycle;
\draw (2, 0)--++(2,0);
\draw (0, 2)--++(4,0);
\draw (2,4)--++(0,-4);
\draw (4,2)--++(0,-2);
\end{scope}
\node [fit=(a),inner sep=0pt,draw] {};
\end{tikzpicture}
\end{document}

Or, given the local bounding box, use a rectangle path:

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture}
\begin{scope}[rotate=-{30},local bounding box=a]
\draw (0,0) |- (4,4) |- (6,2) |- (4,0) |- (2,-2) |- cycle;
\draw (4, 0) -| (2,4)
      (0,2) -| (4,0);
\end{scope}
\draw (a.south west) rectangle (a.north east);
\end{tikzpicture}
\end{document}

(This shows the use of -|/|- paths to cut the number of coordinates in half.)

If drawing the same lines more than once isn't a problem, you could use a loop like this to draw the shape:

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture}
\begin{scope}[rotate=-{30},local bounding box=a]
\foreach \x/\y in {1/0,0/1,1/1,2/1,0/2,1/2} % list of rectangle centers
   \draw (\x-0.5, \y-0.5) rectangle ++(1,1);
\end{scope}
\draw (a.south west) rectangle (a.north east);
\end{tikzpicture}
\end{document}

Addendum

Perhaps the easiest way to achieve your additional requirements is to use nodes to make the squares, and a fit node to make the rectangle. By filling the nodes with white, and using on background layer to fill the fit node with some other colour, you get the appearance you're asking for. If you actually want to fill only the area between shape and rectangle you need to use \clip in a scope, and I'd actually suggest asking a new question.

Because everything is a node, drawing lines between inner squares and outer rectangle is easy, just use the node anchors as coordinates.

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{backgrounds,fit}
\begin{document}
\begin{tikzpicture}
\begin{scope}[rotate=-{30},local bounding box=a]
\foreach [count=\i] \x/\y in {1/0,0/1,1/1,2/1,0/2,1/2} % list of rectangle centers
   \node [transform shape, % allow for rotation
          draw, % draw outline
          fill=white, % fill with white
          minimum size=1cm, % set size
          name=n-\i,
          %label=center:n-\i % if you want to see the names of the nodes, uncomment this
          ] at (\x-0.5, \y-0.5) {};
\end{scope}
\scoped[on background layer] % the following path is on the background layer
  \node [draw=black, fill=blue!10, fit=(a), inner sep=0.2pt, name=frame] {};


\draw [-latex] (frame.280) to[bend right] (n-1);
\draw (frame.east) -- (n-3.north east);

\end{tikzpicture}
\end{document}