How are ancient Greek values like hubris (extreme arrogance) and arete (fulfilling one's potential) reflected in The Fountainhead?
I think that the difficulty in answering this question lies in the understanding of the Greek terms and values.
Hubris, in classical Greek does not mean "extreme arrogance" (despite the common misuse in 20th century popular culture). Instead, it is a legal term, similar to the Latin "vis", meaning something close to aggravated assault. It was not considered a value in Greek culture, but rather a vice. Thus the arrogant behaviour of many of the characters Ayn Rand idolized would have been considered examples of lack of the virtue of sophrosyne, or self-control (moderation is also a possible translation), something on which, according to most Greek philosophers, most other virtues depend.
Arete does not mean "fulfilling one's potential" in a modern sense, but rather excellence. It can mean excellence in a specific skill (e.g. the excellence of the wrestler in wrestling) or the excellence of the human qua human, which consists of exercising one's reason, as that is the only specifically human activity.
While Rand in some ways follows Nietzsche, she's much closer to the antagonists of the Platonic dialogues (Callicles, Thrasymachus) than to those characters held up as models of virtue in Greek culture.