muslim law of inheritence

Whenever a Muslim dies, all his property whether acquired by him during his lifetime or inherited from his ancestors can be inherited by his legal heirs. Subsequently, on the death of every such legal heir, his inherited property plus the property acquired by him during his lifetime shall be transferred to his heirs.

Female lrs get half of male share in Islamic law.

See, first of all there's no distinction between ancestral or self-acquired property under muslim law, and thus the property is distributed as per Shariah Law. Now, as per Shariah Law the share of a male heir is twice of that of a female heir (be it wife or daughter).

The answer to your questions are:-
1.) property goes to all legal heirs as per the share explained above.

2.) No children and mother have unequal rights. Male heir (son) has twice of that of a female heir (i.e. wife or even daughter).

3.) Mother can not give the property to a sole heir as she's not the sole owner of the property. This could only take place in case the father (deceased) have formulated a Will before his death as per which he have given all rights of the property to his wife only.

Hope It's Clear!

Regards,
Kevin M. Paul

The query is too speculative to suggest any meaningful suggestion. All that could be stated that under Muslim Law, inheritance opens up only after the lifetime of the holder of the property.