On connecting combinatorial rectangles
It's not possible.  Consider the following 3x3 boolean matrix:

1 1 0

1 0 1

0 1 1

For every pair of rows {r,r'} , there exists a column c such that {r,r'} X {c} is a combinatorial rectangle.  For any particular pair, we can permute the rows such that {r,r'} are adjacent.  However, since we have a combinatorial rectangle for all pairs of rows, it's not possible to permute the rows so that all such rectangles are geometrically connected simultaneously.