How is phase defined in a binary orbit with eccentricity? Are orbital phases of the black spot in the figure measured from some angle or time/period?
Usually, how is phase=0 defined? It is relative to the line of apses perhaps with phase=0 at periastron?
Any of the anomalies below is defined as orbital phase? Please specify reference papers or books.
E: eccentric anomaly
M: mean anomaly
u: true anomaly

Source
Usually, how is phase=0 defined? It is relative to the line of apses perhaps with phase=0 at periastron?

The true anomaly, $\theta$, is the angle between the current location of the orbiting particle and its location in the orbit at which it is closest to the central body (called the periapsis/periastron). The word &quot;phase&quot; is used variously in physics and astronomy, but based on your question, you may mean $\theta$ since it is defined as being zero at periastron.

Are orbital phases of the black spot in the figure measured from some angle or time/period?

It ultimately depends on how you want to compute the trajectory/orbit of the particle (i.e., the black &quot;spot&quot; in the OP image) that is moving about a primary body (i.e., the star in the OP image). Alternate values can be used instead of $\theta$, for example $\displaystyle M$, the mean anomaly.