My father also earned some property on his own. Can he execute a will to my brother alone for the same as he wishes.
Yes he can do that, you cannot stop him, at least legally, from doing so.
Can I seek legal rights in this property.
You are not entitled to any rights in the property, hence you cannot claim any share in it legally at least during the lifetime of your father.
Or can my daughter aged 18 years can claim legal rights for share in the same.
You yourself do not have any rights in the property, from where shall your daughter get such rights?
There is no concept that grandfather's property shall be shared by grandchildren.
It is available only on ancestral properties.