Who tests a module with the action item from quality assurance, the QA team or the developer?

The developer should use them in the development and when the tests and processes are finished, the QA team should have a "qualiy approval submissal" of modules that the module developer would like to have a "stamp of quality"

Kindof like the XHTML validation. When developing, the developer continually uses this test to check the code. When it is finished, a link to the validator can be provided so everyone can see that it is so. Now, the XHTML validation is an automated process and therefore it can be done that way. The QA team is not a machine and therefore it will have to be a more controlled process to get the "stamp of quality" (or whatever it will be called by the QA team) since it will be a potentially large task for the QA team.
This is also why the module developer should do as much as possible beforehand and only submit a module for testing that he or she believes will pass it.

How many items on the "module QA test" can a module fail and still be considered "quality"?

That still needs to be defined by the QA team.

A small note to the team developing the QA test:
In the OK and NOK columns, you should make the font size a big uniforme size, so that us developers can see the X. I'm assuming that we're supposed to place an X correct?

Another small note:
At the bottom there should also be a developer comments box, so that we (developers) can place some general comments about module wich is submited to the test.