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I see no mention in Transferring Runes about requirements, but there are requirements for Etching Runes. It's unclear (to me) that the two are directly related.
In order to transfer existing Runes, do you need
Transferring runes uses the Craft activity and inherits its requirements. This includes the Crafting Proficiency stated in the rune entry and the Magical Crafting feat, since runes provide magical enhancements and therefore (at least to my mind) should be considered magical. Both the Craft activity and the Etching Runes sections also mention the formula as a requirement (while one could argue that you might be able to use the existing rune as a blueprint for the transfer, the formula is so cheap compared to the rune, that I don't see much of a point arguing over this).
As to the relationship between the Transferring Runes and Etching Runes sections: The former is a subsection of the latter and therefore inherits all of its rules, except when directly overridden. Those, however are mostly copied from the Craft activity which they also refer to, so they don't seem to have a big impact on their own.
Therefore I would rule that, indeed, all requirements you stated do apply.
