What did we learn with Nazi human experimentation?
Basically nothing.  The Nazis did unfathomably terrible things of little value, and they did it poorly.

This* is a fascinating, albeit long, read.  It goes through some of the ethics of the data, but first lists some more of the "experiments" the Nazis performed.  To add to your list: high-altitude, sea water potability, tuberculosis, poisoning, artificial insemination, and numerous woundings.  They also did terrible things to twins.  Aside from being torturous and cruel, the "experiments" rarely if ever used anesthetics and were usually designed to kill the prisoner.

The article goes on to list a few case studies where some of the Nazi works came up and could have been considered, but were repeatedly shot down.  It then details a number of reasons why the "experiments" were worthless.  In particular,


"[I]t is doubtful that physiological responses of the tortured and maimed victims represented the responses of the people for whom the experiments were meant to benefit."
Nazi "researchers" were racists who were looking to validate their own beliefs.  No good science comes from that.
The results weren't ever actually published.
The "data" are inconsistent.


The article moves into ethical arguments and hypotheticals, but ends up saying theoretically some of it could be considered, or that "Absolute censorship of the Nazi data does not seem proper, especially when the secrets of saving lives may lie solely in its contents."  It's a complicated scenario where that would arise.



Editing a few years later to add this discussion from the NY Review of Books.  It's a little removed in tone, and is over-generous as regards the intent of the Nazi torturers, but makes the interesting point that one good thing to come out of the experience was the first codified guidelines for human experimentation:


  As part of the judgment, the court issued the celebrated Nuremberg Code in 1947—the first, shortest, and in many ways most uncompromising of the major ethical codes and regulations for the conduct of medical research on humans. Although the code had no legal authority in any country, it had great influence on ideas about human experimentation, and subsequent international codes and legislation.


In particular, the concept of "informed consent" is directly traceable to the Nuremberg Code:


  The first provision of the Nuremberg Code is unqualified: “The voluntary consent of the human subject is absolutely essential.” No exceptions are permitted... Furthermore, the code is clear that consent must be given by subjects who are fully informed.




*I should note that the article is from a Jewish law website, so some may discount that as not a perfectly neutral source.  Which is silly.