The responsibilities of a Project Assistant vary widely and should be stated clearly at the time of hiring in a position description that defines the general parameters of the work. Depending on the kind of work they do, they may work more or less autonomously, and undertake more or less ambitious and difficult work.
Beyond the scope of their work, Project Assistants typically work in professional and administrative environments, so they are responsible for conducting themselves according to the professional standards that apply. This will always include timeliness in reporting to work, email decorum, and professional interactions with colleagues and those served by the hiring unit. Appropriate dress is also required, but may vary considerably depending on the position.