1. first of all neither she nor your child nor you yourself can claim any share in your father's property as a right, therefore there was no necessity to bequeath the properties by executing a Will. Moreover this can be enforced only after his lifetime.
Therefore you can comfortably ignore her ill-knowledge and illegal claims.
No claim by her in this regard is maintainable in law.
The Will even if it is unregistered is valid if witnessed by two attesting witnesses.
2. Not only your father's property but also your property is very safe and secure.
She cannot claim any share in it as a right even on behalf of your child, hence you do not have to do anything about it.
3. From your contents it can be seen that it is not ancestral property but it can be treated as his own and absolute property,hence he can very well transfer the same to his daughter by a will or even by a registered gift deed.
4. Dont stretch your imagination too far, nobody's life and death is in their hands.
However, she cannot legally claim any share in the property if they have been settled or disposed during the lifetime of its respective owners.
She can ask for maintenance from her husband alone and not from others.