The correct option is "1 and 3 only." Annie Besant indeed played a pivotal role in the Home Rule Movement, advocating for self-governance in India while promoting political awareness among Indians. Additionally, she served as the President of the Indian National Congress in 1917, marking a significant moment as she was the first woman to hold this position. However, while she was involved with the Theosophical Society, she did not found it; rather, it was established by Helena Petrovna Blavatsky and Henry Steel Olcott in 1875. This distinction is crucial in understanding her contributions to Indian nationalism and social reform, highlighting the interconnectedness of various movements and figures in the context of India's struggle for independence.