People with an external role can’t create or edit tasks.
Tasks can only be created by, edited by and allocated to internal roles. This is one of the core things that differentiates client roles and internal roles in Project.co.
You can see more information about the different roles and what they can do here: https://www.project.co/learn/kb/roles-permissions/
The reason for this is that Project.co is designed to facilitate the process of working with clients. We assume that your business is doing work for the clients business. Therefore tasks are allocated to internal people so they can do the work required to complete the task. People with external roles can see the task name and due date but they can’t see any other information regarding tasks or engage with them.
This makes it clear what will be done and when for client but they don’t have the ability to edit or change tasks.