Let's analyze the statements based on Section 2 of the Hindu Marriage Act, 1955 (Applicability of Act):
Statement I: This is largely correct. Section 2(1)(c) states the Act applies to any person who is not a Muslim, Christian, Parsi or Jew by religion, unless it is proved that they would not have been governed by Hindu law. It does not mention 'Santhal', but Santhals are animists and are generally governed by their customs, but the negative definition is broadly true for the purpose of the Act.
Statement II: This is correct. Explanation (a) to Section 2(1) clarifies that any person who is a Virashaiva, a Lingayat or a follower of the Brahmo, Prarthana or Arya Samaj is a Hindu for the purposes of the Act.
Statement III: This is false. The Supreme Court has held that a person who was a Hindu and converted to another religion can revert to Hinduism by simply declaring their intent to do so and conducting themselves as a Hindu. There is no requirement for any specific expiatory ceremony, ritual, or custom unless the person's community insists on it. The intention and acceptance by the community are key.
Since the question asks for the false statement, III is definitively false.