A HashSet uses a HashMap internally that has a default capacity of 16 and a load factor of 0.75f. The capacity is not a hard limit after which no more elements can be added. The HashMap maintains an internal threshold flag that, when reached, triggers a resize action, which results of a new capacity that is equal to the capacity multiplied by the load factor.
Q1: Correct, for all intents and puroses, the capacity of the HashSet is dynamically increased.
Q2: The size, as in number of elements in the HashSet, can be easily retrieved using the HashSet.size() method. There isn't really an easy way to retrieve the capacity, but there's really no need to either. If you absolutely desperately want to, I guess you could retrieve the backing HashMap using reflection and determine the capacity of the HashMap in the same manner.
Build a man a fire, and he'll be warm for a day. Set a man on fire, and he'll be warm for the rest of his life.