Einstein's Cat said:
Is the amount of dark energy in the universe constant or else does it increase as the universe expands?
What do you mean by "amount of dark energy"? The
density of dark energy is constant. But the
volume of the observable universe is increasing, so multiplying the constant density by the increasing volume gives an increasing
total quantity of dark energy. However, the latter quantity isn't really meaningful physically; it's the density that matters.
Also, the density of ordinary matter, dark matter, and radiation is
decreasing as the universe expands, so, as Bandersnatch said, the density of dark energy
relative to the other densities is increasing. But that reflects a change in the other densities, not in the density of dark energy.
Einstein's Cat said:
Doesn't that mean that the cosmological constant isn't constant?
No. The cosmological constant is equivalent to the density of dark energy, which is constant.