What are some characteristics that demonstrate continuity between
the old, Western Roman Empire and the new, Eastern one
beginning in the 4th century CE?

Protecting and assisting  u.s. citizens  living or traveling abroad; assisting u.s.  businesses  in the international marketplace; coordinating and providing support for international activities of other u.s. agencies (local, state, or federal government), official visits overseas and at home, and other diplomatic efforts.keeping the public informed about u.s. foreign policy and relations with other countries and providing feedback from the public to administration officials.providing  automobile registration  for non-diplomatic staff vehicles and the vehicles of diplomats of foreign countries having  diplomatic immunity  in the united states

What are the options

Unfortunately, this question is made for an opinion, so you'll have to answer based on your experience.. for the