As per section 22(3) of the CGST Act, the transferee or the successor, as the case may be, shall be liable to be registered with effect from the date of such transfer or succession, where a business is transferred to another person for any reasons including death of the proprietor. While filing application in FORM GST REG-01 electronically in the common portal the applicant is required to mention the reason to obtain registration
2) you can continue the business after changing the bank account , PAN card in your name . father bank account will be closed by the bank