If dark energy is everywhere around us, then why don't we get separated? For example why don't I get separated from the pen kept in front of me? Or take a similar example in free space. Is dark energy's power greater than gravitational power?
The density of Dark Energy is not very high. In a place with lots of matter, the attractive forces of gravity are greater than the repulsive forces of dark energy. In mostly matter empty space, the repulsive forces of dark energy are much larger than the attractive forces of gravity.
Dark energy is responsible for the acceleration of the universe at large scale, that is, it causes the second derivative of the cosmic scale factor $a(t)$ to be positive. But a smaller scales we found agglomerates of particles where the effect of the four forces (not only gravity) is much stronger that the repulsive effect of dark energy. A useful analogy which can help to understand what's going on is that of the raisin bread where a bread is expanding on the oven but the raisins on it (the agglomerates of particles) do not expand.
Gravity and dark energy would have to be one & the same, due to the fact that gravity is spacetime and space time is basically the mother board or rather the rawness or better, the naked form of the universe.
If einstein is correct about spacetime curvature than both are just different movements of the same entity, sort of like, how a river moves forward, all while bumping into stones, splitting them and emerging into larger aquatic bodies.It still remains the same water no matter what the direction and the pull of gravity is, similar to a river becoming stagnant as the water seeps into the rocks, its curving around.
So dark energy and spacetime may be the same river representing space with a liquid light quality or an invisible light that behaves like water as a whole.