1. The sale was executed more that 30 yrs ago on four 5 Rs stamp paper's in the presence of 3 witnesses.
The unregistered sale deed is not a valid title document.
2. The witnesses and Seller who took part in transaction are NOT ALIVE and we dont know the wherebouts of seller's family.
First send a notice to the seller to his last known address by registered post asking the seller to execute a registered sale deed in your mother's favor. Let the notice return undelivered with remarks no such addressee or addressee left etc., then you may issue the same notice through a newspaper publication in a local newspaper, secure this evidence.
3. Is it Possible for my mother to get the house registered with the sale deed in registrar office on her name ? if yes then what will be the procedure ?
your mother can file a suit for declaration of her title on the basis of the evidences so created as suggested above and then get the property registered through court itself.
4. if she cannot register on her name , Is it possible for any of the son to raise objection to her decision of partition as some of the children are demanding certain portion of the house? Or is it possible for any of the children to challenge the ownership of the house ?
First she has to acquire the property legally and then she can decide abut distributing the same to her children or to anyone of her choice as per her desire, nobody can legally dispute her decision to disburse the property as per her desire.
5. If she decide's to execute the registered partition deed on the name of 4 children out of 7 in registrar office, will that settle the matter permanently in all legal aspects ?
Read the above answers which will clarify this question too.