An act of a in the ordinary course of business of the company makes the other directors equally liable as the one acting. this is based on the principle of fiduciary relationship and agent relationship. the other directors of the company are equally liable with the acting director generally. however, there is an expection, if it can be established that the consent of the director was given to the said act and the same was done without his knowledge and accent.
further regarding resignation, the procedure is generally given in the Articles of Association of the company and in case it is silent on the resignation, a director can resign by sending a resignation to the chairman of the board of directors. the intimation of the resignation to the registrar is to be filed by the company by way of filing E-form 32 within 30 days from the date of resignation. it is suggested that you first check the Articles of Association of the company if there is any clause as to resignation by the directors ans in case it is silent then you should send a resignation letter to the chairman of the board of directors at the registered office of the company stating that he (director) hereby resigns from the post of directorship with immediate effect i.e. date of resignation. the letter should be sent by registeres post A/D or if given by hand then a receipt of the same should be taken (signature of the person authorised to receive mails in the company and receipt stamp of the company). thereafter the director shall be liable only for the actions taken by the company till the time he submitted his resignation which can further be defended as said above on the grounds of consent and knowledge of the action.
i hope this answers your concern.