If one wanted to be even more pedantic, N is the modulus, e is the public exponent and d is the private exponent. N is required for both public and private operations.
Yes. But is there a more general (or specific, depending on one's point of view) term that applies to (public key) cryptography? Eg "some random, public, non-repeated stuff" is a nonce, a key is a parameter to an encryption function etc. Ecc keys are over a certain [ed]curve - so you need parameters for that too, but modulus while entirely correct mathematically, doesn't really capture the essence of N from a cryptographic point of view. Maybe just "public parameter"?
