Yes. More precisely, consider the definition from "Elements of the Theory of Computation," 2nd edition, by Lewis and Papadimitriou, p. 37:

So, for a set B to be closed under R, the relation R has to be on the superset of B. In particular, if L' is the closure of L under R, R is a relation on words.Let D be a set, let and let be a (n+1)-ary relation on D. Then a subset B of D is said to be closed under R if whenever and .

Union is a ternary relation onlanguages, not onwords.

Yes, when concatenation is considered on words, not languages. In fact, L* is defined as the closure of L under concatenation (plus the empty string).

Again, (M, M*) is a binary relation on languages.