Mike Toews

Use ST_AsText(geom)

http://www.postgis.org/docs/ST_AsText.html

-Mike

I have an add-on function[1] to return N, NW, W, SW, S, SE, E, or NE
from an azimuth direction. E.g.:

SELECT ST_Cardinal_Direction(ST_Azimuth(A.geom, B.geom))
FROM A, B
WHERE ...

The function can be changed to instead return 'east', 'west', 'south',
or however you want to define.

-Mike

[1]  http://trac.osgeo.org/postgis/wiki/UsersWikiCardinalDirection

Sounds like you have a finite element mesh with nodes and elements.
You can use ST_Relate with pattern 'FF2F11212' to pick out elements
that share the same edge. This DE-9-IM is sort-of a custom ST_Touches,
but only takes linear boundary overlaps. So if you have a table
"elements", and you want to find ones that touch ID 567:

SELECT elements.*
FROM elements, elements as e
WHERE e.id = 567 AND
    ST_Relate(elements.geom, e.geom, 'FF2F11212');

I'm not certain about your second question.

-Mike