Like suggested by one of this question's (or so I understand the meta.discussion), this question should be given some too-many-subquestions-redacting, in particular since the easiest sub-question (0) of it has been answered by myself after another pass over the original literature and its subquestion (3), which can be seen to not be covered by the main question's title has been kindly answered by one relevant literature reference in a comment by F. Ziegler. (I would find more references to systematically ordinal-comparing references useful, though.) I therefore created this satellite question, taking the advice of M. Katz to post it in this forum, leaving the original subquestion in this question in place, but with an edit saying that these questions should be answered here, and repeating them here:
(1) Are there scholarly references (or possibly, testimonies from people having attended those lectures) about whether Zermelo defined the natural numbers this way in his lectures in Göttingen and Zürich? (It of course seems unlikely that he did, having been much involved in axiomatic set theory, and having received what is now the standard definition from von Neumann.) NOTE: This question was first asked here.
(2) Are there scholarly references about whether Zermelo ever publicly discussed, in lectures or in writing, von Neumann's definition, possibly comparing his definition to his own? EDIT: This question was first asked here.