This branding iron is from the Edo period.
Standard spelling with okurigana; widely used for both the mark and the tool.
Kanji-only spelling; common in formal or compact contexts such as official documents or product descriptions.
Compound of 焼き (yaki, 'burning') + 印 (in, 'mark'). The exact historical derivation is straightforward; the word has been used for physical branding since at least the Edo period.