The Regulation does not define the term, and the national identification number serves as the paradigm example. The defining feature in the text is general application, that is, an identifier used across contexts and sectors to identify the same person, which is what creates the linkage risk the safeguard requirement addresses.

No. While the decision to lay down specific conditions is optional ("may further determine"), once a Member State does so the second sentence requires that the identifier be used only under appropriate safeguards for the rights and freedoms of the data subject. The safeguard condition is therefore the price of exercising the option.

No. The words "further determine" show that national conditions come on top of the Regulation, and the closing reference to safeguards "pursuant to this Regulation" confirms that the general regime, including the lawfulness requirements of Article 6, continues to apply to processing of the identifier.

The national identification number is then processed under the ordinary rules of the Regulation without sector-specific national conditions. Article 87 is an enabling clause, so the absence of national rules neither prohibits nor privileges the use of such identifiers.