Legal Rights of Wife's kids from earliar marriage

My mother was a widow with 2 kids(both sons) and my step father was a widower with 2 kids. My biological father expired when we were very young(below 5 years). My mother got remarried when we were around 10 years and he had grown up kids who were out of house on their own means by than. My step father told my mother and grand parents that he has a house on his name and that would be given to his biological kids and he said he will support one of her kids for education to his capacity from his earnings. Everyone(my mother and my grand parents) agreed as we were looking for a helping hand due to our financial conditions. However no written agreement was done. Marriage went fine after couple of years, out of love towards my mother my step father allowed my brother to join him as well and he took care of our(both of our brothers) food/shelter & study. We both have studied until post graduation with his support. He even helped us financially with a few lakh rupees when me and my brother brought land and built a house on it. We have even received some property & money from our paternal grand parents too towards settlement of my father's share in their property. Looking at my step's father love towards my mother her biological kids asked to gift the house(as promised) as they felt he will not keep his promise and spend all his money on her and us and die inestate. My mother opposed to it as she feel his biological kids are well settled and have earned enough money on their own. She wants 50% of share in the house equivalent to share of his first wife kids. Also she fears her survival after my step father's demise. After a lot of negotiations, my step father decided to buy an apartment for which his kids will contribute 50% and rest 50% would be spent from his retirement benefits. The house will be on both my step father's and my mother name. And it would be her shelter after my step father demise , in the same way it will be his shelter if my mother demise first. My step father will be left with a 20 lakh rupees in bank which he will be doing joint FDs, he also get pension to meet every day needs. However my mother fears that his kids will come and claim the apartment after his demise, so asked his kids to sign an agreement where in they state that they wont have any rights on the property and will never claim it after his demise, however they want us(her kids) to do the same as the property is on her name too. I mean they want us to write in writting that we will not claim anything incase our mother demise first. Right now my mother is not agreeing to it(for various reasons) Notes: 1) My step father never adopted us offically, we have used our bioligical father name in most of records. 2) My mother is not much educated, never had any earning of her own or brought any dowry/property share from her parents. However our maternal grand parents have given some land and money to us. 3) We received some money/property from bioligical father's family too as settlement towards my father's share in my paternal grand father's property. Questions are: 1) Do we have rights to the apartment or bank FDs in which my mother is a co-owner? Is it correct my step father's kids to fear? 2) My mother wants to gift the apartment to us after my step father demise, will there be any issue? 3) What if my step father includes the clause in the apartment sale agreement itself that, incase one co-owner demise, other would be absolute owner of apartment. Is that suffice to keep his kids away from apartment? 4) What happens if either my mother and step father demise in-estate. Will both his kids and us will have equal share in the apartment? We are Hindus.