Father earned property distribution in sunni muslim law

1. Is that possible to distribute/partition property equally among all us as father earned property?

=Since the property is self acquired property of your father and your father is still alive, you or your siblings have no right on the property.  Whatever your father decides it will happen.  If you can convince your father and get to an understanding.

2. Shop comes under satta prakar b which is reward from Sansthan which can not be transferred in my name? What I do in this case?

=answered above.

3. Father is deliberately not doing partition equally. Can I stop him through court legal procedure?

=answered above

4. Father is not ready to distribute property among sisters too. Can sister has rights to get the property?

=No, sisters will not have any right as it is self acquired property of your father.

For futher doubts contact me to my email.
 

This being the self acquired property of your father, nobody has any rights in it during his life time.You or your brothers cannot decide about partitioning the properties as per your own will and wish during his life time.  Actually the family partition is a mutually agreed partition in which there is no necessity to follow the legal rules strictly that the properties shall be equally partitioned, there can be many agreements and arrangements for different provisions in the future according to which the partition may come into effect.  However in this situation, during your father's life time nobody has any right hence try for an amicable settlement.