Learn English – Looking seductively at someone

I suppose "I" (is that still Gopal?) is feeling awkward or embarrassed and looking downwards to avoid meeting Aarti's father's eye.

In such an instance, the idiom is to stare at the floor. From the dictionary definitions you give, Gopal is looking fixedly at the floor, probably at a particular point. A gaze is less focused; Gopal would gaze at Aarthi across a crowded room — it's the admiration or thought part of the definition which makes the difference.

Haughty (“Conveying in demeanour the assumption of superiority; disdainful, supercilious”) and supercilious (“Arrogantly superior; showing contemptuous indifference; haughty”) seem relevant, along with some of the other terms in those definitions (eg arrogant, disdainful, and contemptuous) along with related words or phrases like holier-than-thou, sanctimonious, hoity-toity, and stuck up.