Who will be legal hiers

As the property is self-acquired by your father, only option 1 is applicable here i.e. you, your siblings and your mother being the legal heirs of your deceased father is entitled to claim the property share.
Thanks.

A.Dear Sir,
Section 8 of Hindu Succession Act:
General rules of succession in the case of males.―The property of a male Hindu dying intestate
shall devolve according to the provisions of this Chapter:―
(a) firstly, upon the heirs, being the relatives specified in class I of the Schedule;

CLASS I
Son; daughter; widow; mother; son of a pre-deceased son; daughter of a pre-deceased son; son of a pre-deceased daughter; daughter of a pre-deceased daughter; widow of a pre-deceased son; son of a pre-deceased son of a pre-deceased son; daughter of a pre-deceased son of a pre-deceased son; widow of a pre-deceased son of a pre-deceased son.

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1) Your father's self acquired Flat in absence of any Will, has been devolved upon your mother,you and your brother. It is necessary for three of you to obtain Legal Heir Certificate through Declaratory Affidavit enclosing therewith three of yours identity proofs,your deceased father's identity proofs and your father's death certificate and to apply for mutating three of your names in the Record of Rights in the place and stead of your deceased father.

To get the sum kept in your deceased father's bank account ,it is necessary to apply for Succession Certificate,however,if there is any Nominee and if no objection has been raised for disbursement of that sum in favour of that Nominee,such sum of your father's bank account will be given to that Nominee upon filing of your father's death certificate and Nominee's identity proofs before the Banker.

2) and 3)--Not applicable.

Hi,
Since, the property is self-acquired by your father, only the legal heirs of your father will be entitled for the share. Therefore, only the your siblings, your mother and you yourself can claim the share.
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Hi,
The legal heirs of your grandfather, i.e. step-mother and her children, the your fathers siblings can only claim the share in the ancestral property. The self acquired property can only be claimed by the legal heirs of your father, i.e. you, your siblings and your mother.
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Kindly be informed that as far as the self acquired property of your father is concerned such property in the absence of any testamentary disposition would be inherited as per the succession law governing you on the basis of your religion. If you are hindu then the hindu succession act 1956. According to the act your father's class I (one) heirs would include your mother and your two sibling and all three of you would take the property simultaneously. This would be for both moveable and immovable property.

Hence option 1 would be the correct alternative.