Dralasites do indeed have -and always had - internal organs; they are multicellular organisms, not single-celled. But inside their skin, their internal organs were suspended in a generally viscous-fluid-like area.
As for breathing, I think their skin was a bit more active at extracting oxygen than simply using passive osmosis.
Their structure seemed monocellular because of the way their various vital organs sort of "floated around" inside them, but in fact their outer skin moved and changed shape due to a nework of muscles in and just underneath the skin, and the near-syrup consistency of their gel-like interior flesh.
The illustration of hte Dralasite on WOTC's website seems to indicate that their days of translucency have gone the way of the dodo, so instead of seeming like a giant amoeba, they should just be the amorphous blobs they always were, IMO at least. ^_^
What's funny is ... d20 Future's resurrection (? exhumation ?) of Star Frontiers is about 60% of the reason I just bought the d20 Modern rules last week. ^_^ Liking the base class / advanced class mechanic is most of the remaining 40%.