ROW SEPARATION
For the row spacing, instead of specifying a matrix-wide row sep, use the optional argument to \\
to accomplish row specific skips.
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\matrix[column sep=5mm]
{
% Row 1
\node {1:1};&\node {1:2};&\node {1:3};&\node {1:4};;\\[5mm]
% Row 2
\node {2:1};&\node {2:2};&\node {2:3};&\node {2:4};\\[10mm]
% Row 3
\node {3:1};&\node {3:2};&\node {3:3};&\node {3:4};\\
};
\end{tikzpicture}
\end{document}
Alternately, you can keep a default row sep
and specify the deviation from it:
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\matrix[column sep=5mm, row sep=5mm]
{
% Row 1
\node {1:1};&\node {1:2};&\node {1:3};&\node {1:4};;\\
% Row 2
\node {2:1};&\node {2:2};&\node {2:3};&\node {2:4};\\[5mm]
% Row 3
\node {3:1};&\node {3:2};&\node {3:3};&\node {3:4};\\
};
\end{tikzpicture}
\end{document}
COLUMN SEPARATION
As to the issue of column separation, I know of no easy way to accomplish this. In the particular example provided by the OP, the column gaps are all integer multiples of each other. If that were always the case, one can just add blank columns:
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\matrix[column sep=5mm, row sep=5mm]
{
% Row 1
\node {1:1};&\node {1:2};&&\node {1:3};&\node {1:4};;\\
% Row 2
\node {2:1};&\node {2:2};&&\node {2:3};&\node {2:4};\\[5mm]
% Row 3
\node {3:1};&\node {3:2};&&\node {3:3};&\node {3:4};\\
};
\end{tikzpicture}
\end{document}
But I presume that is too much to hope for. The best I could do for the general case is provide the \knode
macro that has an optional kern built in.
\documentclass{standalone}
\usepackage{tikz}
\newcommand\knode[2][0]{\node{#2\kern#1mm}}
\begin{document}
\begin{tikzpicture}
\matrix[column sep=5mm, row sep=5mm]
{
% Row 1
\node {1:1};&\knode[5]{1:2};&\node {1:3};&\node {1:4};;\\
% Row 2
\node {2:1};&\knode[5]{2:2};&\node {2:3};&\node {2:4};\\[5mm]
% Row 3
\node {3:1};&\knode[5]{3:2};&\node {3:3};&\node {3:4};\\
};
\end{tikzpicture}
\end{document}