The correct option is "Only two" because statements 1 and 4 are true, while statements 2 and 3 are incorrect. The 44th Chess Olympiad held in 2022 was indeed the first to take place in India, and the Hamilton-Russell Cup is awarded to the winning team in the women’s section. However, the official mascot was named "Punjab Lion," not "Thambi," and the trophy for the winning team in the open section is the "Trophy of the Chess Olympiad," not the "Vera Menchik Cup," which is associated with women's chess. Understanding these distinctions is crucial for UPSC Prelims as it tests not only factual recall but also the ability to analyze and verify specific details related to events and historical context in Indian sports.