1. Why does eccentricity only vary between 0 and 1?
The eccentricity of an ellipse is, most simply, the ratio of the distance between its two foci, to the length of the major axis.
Why does eccentricity only vary between 0 and 1?

2. The eccentricity of an ellipse is, most simply, the ratio of the distance between its two foci, to the length of the major axis.
For an ellipse the eccentricity is between 0 and 1 (0<e<1). When the eccentricity is 0 the foci coincide with the center point and the figure is a circle. As the eccentricity tends toward 1, the ellipse gets a more elongated shape. It tends towards a line segment if the two foci remain a finite distance apart and a parabola if one focus is kept fixed as the other is allowed to move arbitrarily far away.

3. Which circle has the highest eccentricity?

5. Measuring masses using Kepler's 3rd Law
( m1 + m2 ) P2 = ( d1 + d2 ) 3 = R3
P is the orbital period
m1 and m2 are the respective masses
R = r1 + r2 , the total separation between the centers of the two objects
So if the period P and the average separation R are known,
we can solve for the total mass M = m1 + m2 of the binary system.
If we know enough about the orbits to determine the distances d1 and d2 separately, them the purple [art of the equation above second equation can be used to determine the individual masses m1 and m2.
NOTE: these equations assume that the orbits are circular. If they are more elliptical, the analysis is similar but becomes more complicated.