1. What is legal rights for my mother and all brothers and one sister?
If this property is in your father's name, then it shall devolve equally on all his legal heirs consisting of his wife, and children.
2. Although only one brother and his wife and children are living there permanently with my parents and we all go there on occasions. Do we have equal right on this property?
All the legal heirs of your deceased father have equal rights in the property left behind by him upon his intestate death.
3. As I mentioned that property (house and shop) was transferred to my father's name after death of my grandfather, so it should be treated as ancestral property. So as per law is there any differentiation for who is living there and who not? Or mother and all children have equal right to the property irrespective of my brother and parents only was running the shop and we (other brothers and sister) not?
It is not ancestral property.
It becomes your father's own property and all his legal heirs have equal rights in the property.