They have no other duties. Traffic police are recruited impartially from all citizens of Egypt and religious affiliation is totally immaterial to recruitment. According to a phone conversation with an official in the International Coptic Federation, it is very likely that a Roman Catholic, if accepted in the police academy would, upon graduation, hold a position of a traffic police officer, the entry level point of the police hierarchy. He stated that this law is applicable to any Egyptian position, including police work. He also stated that traffic police do have connection with and influence over crime investigation, not only in the traffic area.
All Egyptian policemen can take any action that they want.
A traffic policeman in Egypt is still a very powerful position. There are many Christians who have Muslim subordinates. So, it is inaccurate to say that Christians cannot be bosses. It is systematic, particularly in the Army, that Christians cannot have authority over Muslims, especially concerning soldiers, promotions and police. Yes, the rule does apply to both positions.