I am aware that membership of the epi is obligatory once I am registered on the list of professional representatives. Will I receive a separate request from the epi to pay the membership fee?

Once you have been entered on the EPO's list of professional representatives, you will receive membership and payment information from the epi. If you have any questions, please contact the epi direct. More information https://patentepi.org/en/the-institute/annual-subscription.html