I can clarify your doubts about the Payment of Gratuity Act 1972 only.
Applicability of the Act
If your school is employing or has employed in the past 10 or more persons, the Payment of Gratuity Act 1972 is applicable to your school.
Whether a Teacher is an Employee or Not
The definition of an employee was amended by Act 49 of 2009, and the amendment was given effect from April 3, 1997.
As per this amended definition, "Employee" means any person (other than an apprentice) who is employed for wages, whether the terms of such employment are express or implied, in any kind of work, manual or otherwise, in or in connection with the work of a factory, mine, oilfield, plantation, port, railway company, shop, or other establishment to which this Act applies. However, it does not include any such person who holds a post under the Central Government or a State Government and is governed by any other Act or by any rules providing for the payment of gratuity.
Your school authorities said that you are not eligible, perhaps based on a judgment "Ahmedabad Private Primary Teachers v. Administrative Officer (2004) 1 LLJ 596 2004 LLR 97 (SC)," which observed that even though the Government extended the Payment of Gratuity Act to educational institutions by its notification dated April 3, 1997, teachers, not being "employees" under the Act, would not be eligible for gratuity.
With the amendment of the definition of "Employee" with effect from April 3, 1997, the "teacher" is entitled to gratuity.
Case Laws
1. A teacher being entitled to gratuity can get it w.e.f. April 3, 1997 (Mahendra Singh Chabra v. Appellate Authority, Payment of Gratuity Act, Indore 2011 LLR 980 (MP HC)).
2. Non-Governmental educational institutions are bound to pay gratuity to their employees (Shri Agawral Shiksha Samiti v. Moti Chand Jain, 2009 LLR 401 (Rajasthan HC)).