Is there a printed map / tree / graphic of a sample array(s) during each phase? This is a larger question to help me better visualize the Drupal array structure at each 'stage' of the life cycle. I'm looking for material to help me see what's happening behind the scene that center on the array structure exposed to the various hook calls.  

Does anything exists in this fashion? I guess something could be pieced together by examining the APIs, but at it's core (version 7 at least), Drupal is about letting various components authored by different individuals to flexibly alter array(s) before their final HTML render.
Devel is a good place to start. That will make the function dpm() available to you. This will allow you to print out arrays in an extremely user friendly visible way. If you're doing any sort of development you should really look into this module. I know when I'm trying to figure out what's being called for a given area I often use the combination of dpm and debug_backtrace.

There's also a theme developer that relies on Devel that you can you to see a back trace of functions.