Q.Which of the following best describes a Giffen good?

A Giffen good is defined specifically by demand falling as price falls, due to a dominant income effect on a strongly inferior good. …

Examining each option against the definition of a Giffen good:

1. Zero price elasticity of demand describes PERFECTLY INELASTIC demand — quantity demanded does not change AT ALL as price changes (e.g. an essential drug with no substitute). This is a different concept from a Giffen good, whose quantity demanded actually moves in the "wrong" direction, not zero direction. Incorrect.
2. An inferior good whose quantity demanded falls when its price falls is exactly the defining behaviour of a Giffen good: it is a strongly inferior good, forming a large part of a poor consumer's budget, where a price FALL raises the consumer's real income enough that they buy LESS of the inferior good and switch to a superior alternative. Correct.
3. A luxury good with high income elasticity describes a good with $E_y > 1$ under NORMAL demand behaviour (price falling would still raise its quantity demanded as usual) — this is unrelated to the Giffen exception. Incorrect. …

Confusing "inferior good" in general (which only requires negative income elasticity) with the STRICTER "Giffen good" condition, which additionally requires the good to violate the Law of Demand with respect to its OW …