Hi,
What's your API problem to achieve your request?
Revit API provides geometry related API to retrieve solid, face, edges and vertexes of element geometry:
http://thebuildingcoder.typepad.com/blog/2010/01/geometry-options.html
http://thebuildingcoder.typepad.com/blog/2010/02/retrieving-column-and-stair-geometry.html
Regarding connection of elements, for example, you can use BooleanOperationsUtils API to get the connection solid of wall and column and then use the geometry API to retrieve your desired geometric information.
http://thebuildingcoder.typepad.com/blog/2011/06/boolean-operations-and-instancevoidcututils.html
Do you think this is helpful?