So, if I chose to build an Unbodied character and drain the hit dice, would it use any of my class ranks? Also, since Unbodied manifest as 4th level Psions, does that give me all of the benefits of having 4 levels in Psion (skill points, etc)? How would I level as an Unbodied and how would I get the Psionic powers that come with being Unbodied, like Mind Thrust?
I don't think you could drain it down past 1 hit die, but it could be argued that if you did drain down to 1 HD that your first level in a class would replace that... (it could also be argued the other way).
As for "all the benefits", no. It just gives you the things related to manifesting (power points, manifester level, powers known, etc). Skill points, hit points, etc, all come from actual
hit dice, not virtual levels of a class.
Mind Thrust is a power the particular example Unbodied chose for his virtual psion levels. It is not required at all. You could pick any powers known that a telepath of your equivalent level could choose.
For example: if you're allowed to effectively exchange all 4 unbodied racial hit dice, and then start out with five actual psion class levels (so your ECL would be 9, with no racial hit dice and a +4 LA), you'd only have the hit dice, feats, skill points, etc of a 5th level psion, but you'd have a manifester level, powers known, power points, etc of a 9th level psion. You'd also still get everything listed in
the "Unbodied as Characters" section (Incorporealness, Assume Likeness, Hide Mind, racial skill bonuses, etc).