Muslim personal act applicability

As per your concerned query!
To answer the 1st questions

In Non-testamentary succession, the Muslim Personal Law (Shariat) Application Act, 1937 gets applied. On the other hand, in the case of a person who dies testate i.e. one who has created his will before death, the inheritance is governed under the relevant Muslim Shariat Law as applicable to the Shias and the Sunnis.

In cases where the subject matter of property is an immovable property, situated in the state of West Bengal, Chennai and Bombay, the Muslims shall be bound by the Indian Succession Act, 1925. This exception is only for testamentary succession.

Inheritance of property in Muslim law comes only after the death of a person, any child born into a Muslim family does not get his right to property on his birth. 

To answer your second question
Under Muslim law, certain requisites make a valid Will that can be competent and capable of taking effect. Thus, the following discussed requirements must be satisfied:

The legator must be competent to make a Will.

The legatee must be capable of taking such endowment.

The property which is endowed by the legator must be bequeathable.

Free consent of the legator and the legatee.

The legator must possess testamentary rights over the property.

If a person making is competent in these circumstances, the father can give his property to the son. The Will made by such Muslims is regulated by the provisions of the Indian Succession Act, 1925 if the immovable located in the state of West Bengal or a property that falls within the jurisdiction of the Bombay and Madras High Courts, and not by the Muslim Personal Act.

To answer your 3rd question
In case of testamentary succession for immovable property which is particularly located in the state of West Bengal or a property that falls within the jurisdiction of the Bombay and Madras High Courts, the succession is conducted as per the Indian Succession Act, 1925.

Under the Indian succession, he would have no restrictions on him to bequeath only 1/3 of his property by a Will as per the Muslim Personal Law.

Hope it is helpful
Regards
Minakshi Bindhani