1. Can this be done with a single mutation application or I have to apply separately for two mutations, once for transfer of the owner's name from original land-owners to my mother and once for myself on succession ground?
A joint application by you and yor mother can be submitted to the competent authority for transferring the property in your name and your mother's name.
In the application it can be mentioned that the original joint owner. i.e., your father died on .... hence his legal heirs being you and your mother are the successors in interest. You can enclose your father's death certificate and legal heir ship certificate obtained from the revenue department along with this application.
2. If it can be done with a single application would I need to submit any affidavit or death certificate of my father should be enough? Does my mother need to submit any affidavit regarding her succession?
A copy of the death certificate along with the legal heir ship certificate issued by the revenue department or a duly notarised family or genealogy tree certificate may be attached. If need be then you can affirm the contents in an affidavit format.