If you're not set on the array
approach and would be okay with explicitly specifying the size of the squares, you could use TikZ for this. Based on the answer to the question TikZ matrix as a replacement for tabular, you could define a style
that adjusts a TikZ matrix
to have all the cells join each other and have identical heights and widths:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\tikzset{square matrix/.style={
matrix of nodes,
column sep=-\pgflinewidth, row sep=-\pgflinewidth,
nodes={draw,
minimum height=#1,
anchor=center,
text width=#1,
align=center,
inner sep=0pt
},
},
square matrix/.default=1.2cm
}
\matrix[square matrix]
{
16 & 3 & 2 & 13 \\
5 & 10 &|[fill=yellow]| 11 & 8 \\
9 & 6 + 2 & 7 & 12 \\
4 & 15 & 14 & 1 \\
};
\end{tikzpicture}
\end{document}

To adjust the size of the elements, use square matrix=<length>
. To fill elements with different colours, use |[fill=<colour>]|
in the cell you want to adjust.
In answer to your first question - mixing colours in (say) RGB format - you could use the notation similar to that specified in the xcolor
package documentation, since TikZ recognizes this. For example, mixing/sharing proportions of black green is obtained using
\node[...,fill=black,...]
\node[...,fill=black!60!green,...]
\node[...,fill=black!30!green,...]
\node[...,fill=green,...]
and displays

Or, if you're interested in mixing certain quantities of RGB colours, you can use a part-wise mix as follows:
\node[...,fill={rgb:red,4;green,2;yellow,1},...]
\node[...,fill={rgb:red,1;green,2;blue,5},...]
\node[...,fill={rgb:orange,1;yellow,2;pink,5},...]
\node[...,fill={rgb:black,1;white,2},...]
which outputs

For answering your second question - dealing with boxes - you can use the fancybox
package or even PStricks
. Here is an example using the latter:
\documentclass{article}
\usepackage{pstricks}
\begin{document}
\begin{pspicture}(5,5)
\psset{fillstyle=solid,framearc=.3}
\psframebox[fillcolor=red]{\textcolor{white}{TEST}}
\psframebox[fillcolor=green!50!red]{\textcolor{white}{TEST}}
\psframebox[fillcolor=black!50]{\textcolor{white}{TEST}}
\psframebox[fillcolor={rgb:red,1;green,2;blue,3}]{\textcolor{white}{TEST}}
\end{pspicture}
\end{document}

Best Answer
Use the simple
\rule
command: