Statement 3 is correct. The Election Commission of India (ECI) possesses the authority to adjudicate disputes concerning the splits and mergers of recognized political parties. This function includes determining the legitimate faction of a party and allocating party symbols as per established precedents and internal party strength.
Statement 1 is incorrect. The Election Commission of India is a three-member body, comprising the Chief Election Commissioner and two Election Commissioners. It was originally a single-member body and transitioned to a multi-member commission in 1993.
Statement 2 is incorrect. The Election Commission of India, not the Union Ministry of Home Affairs, is solely responsible for determining the election schedule for both general elections and by-elections. This power is exercised under Article 324 of the Constitution, which mandates the ECI to ensure free and fair elections.