Is the coxswain part of the crew, and what if a coxed boat finishes without its coxswain?

Coxswains are members of the crew, and any reference to rowers in the Rules includes coxswains unless stated otherwise (Rule 29.1).

A race is valid even if the crew is incomplete. However, a crew of a coxed boat that finishes the race without its coxswain is excluded (Rule 82).

The gender of a coxswain is open: a women's crew may be steered by a man and a men's crew by a woman (Rule 29.2).