Statement 1 is correct: The Katapayadi system, associated with Vararuchi of Kerala (perhaps an early figure or a later one, depending on the specific Vararuchi referred to), was indeed used in astronomical computations, including determining planetary positions, based on mnemonic verses like the Chandra Vakyas. Statement 2 is correct: Achyuta Pisharati (1550-1621) was a key figure in the Kerala School, and Uparagakriyakrama, a text on eclipses, is one of his known works. Statement 3 is correct: The inauguration of the Kollam era (825 CE) is traditionally linked to the Chera rulers of Mahodayapuram (modern Kodungallur). While precise details are debated, the era's origin in this period and region, associated with rulers like Ravi Varma, and the mention of an observatory aligns with the flourishing astronomical tradition in Kerala during the medieval period.