Transfer of property to legal heir

All your queries can be decided upon a meeting with your household members and peaceful talks on the issue.  If nothing fruitful is arrived, then you consult a local lawyer and take his further advise.

1. What is the legal allowable time period to transfer the property to legal heirs post the death of my father ?

--You have not mentioned your religion.  Assuming that you are hindus, there will not be any such time limit.  On the death of your father, the title will pass upon the legal heirs equally.

2. What is the process to be followed to transfer the property to the legal heir ?

--Normally there is no need to get any certificate.  But when to go to sell the property the purchaser will ask you to provide him legal heir certificate (succession certificate).

3 What is the process to be followed if we want to transfer one property each exclusively for each son ?

---The title will pass on the legal heirs equally on the death of your father.

The Governent has no jurisdiction to decide  question of succession  therefore the issuance of the the legal heir certificate is unauthorized  and therefore void . only competent court can give such a certificate after adjudication  of a properly constituted application ., succession  to the property takes place in law immediately on the death of the last holder , therefore there cannot be any question of time limit stated by you , If your father was a Hindu , all class one heirs take equally

I am not a lawyer, but one of my friend faced more or less the same situation.

In case there is NO Registered Will, then please mutually settle the matter between the legal heirs, and then whatever mutual agreement is there.  Execute the Relinquishment Deed (R-Deed) and get it register in the Sub-Registrar office.