The author's point about A being "fixed by" the values of X presumably means a functional dependency of the form X->A. Functional dependencies are the basis of 2NF. It 's important to remember that the concept of functional dependency was developed without regard for nulls and it is an assumption of 2NF (and 3NF, BCNF, etc) that relations consist only of values and not nulls.

The definition of a candidate key as a set of columns that "could reasonably be used as the primary key" is a bit strange. A candidate key is quite precisely a minimal superkey. There is no difference at all between a candidate key and a primary key (or even "the" primary key) so I'm not sure what is meant by a "reasonable choice" in that context. It's a pity the explanation of candidate keys isn't spelt out more clearly because it is very often a point of confusion for some people.