Daughter's right to living father's self-acquired propery

1) Does my father have the right to write a 'Will' to apportion all of his (self-acquired) property's rights to his son (i.e. my brother), without any share to me? If not, what are my rights and the due process to claim my share while my father writes the will?

Your father can do so.

2) If my father sells the same self-acquired property (when he is alive), and plans to handover all the proceeds (cash or purchase of another property as gift  or Will ) to my brother and my brother's children, is that considered legal as per the latest property/inherinace laws concerning daughters? If I have any right to that proceed from the sale, what is that, especially in case my father is un-willing to gift part of the proceeds to me?

It is perfectly legal and you cannot do anything to stop him. 

Your father can legally donate all of his self acquired property to a charitable organization also.... Neither son nor daughter have any right in his property during his lifetime. He can legally make a will in anybody's favor or sell off his property.

Self acquired property can be disposed or transferred to anybody according to his will and wish

you cannot do any right on your father property.