1. The Apollo I disaster occurred because of a combination of moderately bad ideas, rather than one horrendous one, as well as workmanship so bad that it would have been laughable, had the result not been so tragic.
To wit, the wiring and plumbing on that particular spacecraft had been worked and reworked, repeatedly, partly because of design changes, but mainly because it had been ill-fitting in the first place. This led to leaks in the plumbing, and arcing in the wiring. The tolerance for combustibles (and particularly for those that would produce toxic fumes) in the spacecraft had become very lax since Mercury and Gemini. And because with the spacecraft pumped down to the standard U.S. orbital atmosphere of pure oxygen at 5 PSI absolute, air was leaking in through faulty seals (not something you would want to launch into orbit with three people aboard!), the people responsible for the ground test, rather than calling it off, or adjusting the systems to tolerate an atmosphere of ordinary air, they pumped it up to hyperbaric pure oxygen. And then there was the hatch design: in light of the incident with the explosive hatch firing prematurely on Liberty Bell 7 (and Gus almost drowning as a result), they overcompensated, fitting the spacecraft with a hatch that required minutes -- not seconds -- to open or close, and that couldn't be opened at all if the interior pressure was higher than the exterior pressure.
Starting with Apollo 7, Apollo launched with a modified oxygen-nitrogen atmosphere that was gradually replaced with 5 PSI pure oxygen during boost and the first few orbits (I believe the suit atmosphere was still pure oxygen before launch, and Apollo astronauts launched fully suited.)
2. I've seen pictures of this new standard docking ring before; I think Popular Science ran an article about it some years ago.
3. We actually had an androgynous docking system since the late 1970s: the Apollo-Soyuz Test Project, although it used the standard Apollo probe-and-drogue between the Apollo spacecraft and the Docking Module, it used a "ring-and-petal" system, completely peripheral, between the DM and the Soyuz. We never did anything more with it, though, probably because (1) it was the final flight of Apollo hardware, and (2) unlike the Soviet Union, which customarily used aerodynamic nosecones over their spacecraft, NASA customarily designed its manned spacecraft to function as aerodynamic nosecones by themselves (with a tight-fitting "boost protective cover" over Apollo), and three projecting capture petals would have ruined the aerodynamics, or required a looser, heavier, BPC.
In fact, I was under the impression that something like what NASA is describing was already in use for the shuttle docking port.
Once again, Trek leads the way.
