Share in the house property

As per Succession Law X's legal heirs ( wife,son and daughter ) will get equal share i.e 1/3-1/3 each in the property left by X.

Yes Son can relinquish his undivided 1/3 share in favour of his mother or sister or to both by registered release deed.If son receives any consideration then it will not be considered as  release deed but will be treated as sale deed.

The legal heirs of the deceased owner are entitled to an equal share each.

His son can very well relinquish his rights in the property by executing a registered release deed even without taking any consideration.

Yes.  The mother and her 2 children have an equal share in the property.  The son can release his share rights to his mother, sister, or both through a registered release deed without consideration or gift it through a gift deed.

Q 1. 1/3rd share each of them.

Q 2 Yes, s/ he may relinquish her/ his share in favour of any other of them.

It is mandatory to get the Legal Heir certificate first to proceed further in the matter . Many people do it late and find it very difficult to get it . 

Yes.  It is a must.  After submission of an application, the RI will inquire and submit a report to the Tahsildar, and the Tahsildar will issue the legal heir certificate.  Generally, it will take some time, but not be difficult.