(i) It was founded by Raja Ram Mohan Roy: Incorrect. Raja Ram Mohan Roy founded the Brahmo Sabha (later Brahmo Samaj). The Tatvabodhini Sabha was founded after his death.
(ii) The Sabha aimed to propagate the ideas of Raja Ram Mohan Roy: Correct. One of its primary missions was to keep the ideals and teachings of Ram Mohan Roy alive and to promote a rational, monotheistic version of Hinduism based on the Upanishads.
(iii) It promoted a systematic study of India's past: Correct. The Sabha encouraged the study of India's history and ancient texts (especially the Vedas and Upanishads) through a rational lens, rather than through superstition.
(iv) The Sabha was founded by Debendranath Tagore: Correct. It was established by Debendranath Tagore (father of Rabindranath Tagore) in 1839.