Dark energy is a catch all term for whatever is accelerating the expansion. The simplest form of dark energy consistent with general relativity is a cosmological constant, and this is just an energy density per unit volume of space.
The cosmological constant is time independant (and position independant) by definition, that is if it were changing in time or space it wouldn't be called a cosmological constant. You can replace the cosmological constant with a scalar field that is allowed to vary in space and/or time, and this gives rise to other models such as quintessence. It's interesting to speculate about ideas like this, but at the moment there is no evidence that the dark energy is changing, and therefore a simple cosmological constant is consistent with observations.
You need to bear in mind that the cosmological constant and quintessence are just mathematical models that fit the observed data. At the moment there is no theoretical reason to recomend the cosmological constant, quintessence or indeed anything else.
The Wikipedia article you linked discusses the various forms of dark energy. Can you expand a bit on what issues the article leaves you unsure about.
My view is that dark energy is like hot air in a balloon. It's density does not stay constant, but decreases as the universe expands, like every other form of energy.
Like other forms of energy, it would also be subject to the second law of thermodynamics and would cool down, slow down, and get sucked into black holes, converting it's pushing effect, into a pulling effect of gravity.
There's no reason to think it behaves completely differently to all other forms of energy we know about.