Partnership firm can't be a share holder for any company. partnership firm is a association of person , and is better represented by its partner.
So it's like two people holding shares in joint account. So partners who want to own shares in firm's name have to open demat account in joint name along with partnership proof.
The rules for opening a partnership firm is the same for any other partnership firm.
t is mandatory for all firms to apply for registration with the Income Tax Department and have a PAN Card. After obtaining a PAN Card, the partnership firm is required to open a Current Account in the name of the partnership firm and to operate all its operations through this bank account.
The Registration of a partnership firm is not compulsory under Part VII of the Indian Partnership Act, 1932, though it is usually done as registration brings many advantages to the firm. It is optional for partners to set the firm registered and there are no penalties for non-registration