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All very good questions, Mathias. How do we get Paizo to answer them? :-)
Class DC = 10+ proficiency bonus for class DC + class key ability score. I suppose if a class doesn't list "trained in class DC" then it's untrained. So for say a Wizard the Class DC would be 10 + 0 + INT, normally 14. Ordinarily this wouldn't matter, because the Wizard has no class abilities that refer to Class DC. Perhaps an archetype would use this untrained DC if the character is a spell caster. Or perhaps not.
I did notice one odd thing, though I didn't look deeper into it: Champion is the only class that is trained in both Class DC and Spell DC.
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