1. If i file any legal case on my younger father using with the above agrement? Or i have legal rights to share my grand parents property throw court?
If this property belonged to your grandfather then only he has rights to execute a partition deed partitioning the properties lying in his name among the people he would like to allot his property or by a family arrangement or by setlement deed, however all such documents involving transfer of immovable properties shall be registered mandatorily. Any unregistered agreement that too on a white paper is not valid in law and you cannot file any such case agaisnt anyone on that basis before any court.
2. The white paper agrement will legally challenged and agre the court?
It is not valid in the eyes of law.
3. If my mother have any legal support from the law to share my father share?
If it was your father's property then your mother may have a share in it likewise you to have a share as a legal heir to your father
4.If law support us to share my grand parents propery in future if they registered(or will) total property to my young father(s)?
Any registered document involving the transfer of property shall be considered as a valid transaction.
5. If there is any chance to occupy my favored noticed properties in the above agrement if do so there is any legal issues?
Legally you cannot do so.