Electron plasma Can a plasma consisting of only electrons exist in a stable configuration?
I do not mean a plasma consisting of separated protons and electrons, but only electrons in an extreme high density. Systems far out of balance sometimes grow spontaneously to a new balance.
 A: 
Can a plasma consisting of only electrons exist in a stable configuration?

Plasma by definition is neutral:

Plasma is an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero

You ask:

I do not mean a plasma consisting of separated protons and electrons, but only electrons in an extreem high density. 

A gas of electrons is what you are describing.
There exists a solid state model  describing:

On a scale much larger than the inter atomic distance a solid can be viewed as an aggregate of a negatively charged plasma of the free electron gas and a positively charged background of atomic cores.

But it is not what you are describing, as it is overall neutral within the lattice.
A concentration of electrons emitted from some matter could happen and is described as "space charge"

In an electron tube, for example, a negative charge results because electrons that are emitted from the cathode do not travel instantaneously to the plate (anode) but require a finite time for the trip. These electrons form a cloud around the cathode, the cloud being continually depleted by electrons going to the plate and replenished by electrons emitted from the cathode. It is this cloud of electrons that produces the negative space charge.

All such sets would be unstable and disperse due to the electrostatic repulsion. The difference in the coupling constants of gravitation to the electromagnetic one is such that the gravitational attraction can be ignored, even if by some ingenious method such a cloud could be contained.
To generate a high density against the electrostatic repulsion would take a lot of energy and ingenuity, maybe with magnetic fields, but to what purpose?
A: It depends on what you call a plasma.  Most plasmas, as well as most objects we see around us are nearly neutral because any substantial charge imbalance would require a large voltage between the object and the rest of the world.  On the other hand, nothing is truly neutral: The Millikan oil drop experiment establishes that droplets routinely gain and lose an electron or two. According to Wikipedia, the Penning–Malmberg trap confines billions of electrons by a combination of electric and magnetic fields.  Plasma physicists study that device and even call it a plasma.  See, for example: Notte, J., and J. Fajans. "The effect of asymmetries on non‐neutral plasma confinement time." Physics of plasmas 1.5 (1994): 1123-1127.
A: The electrons in a conducting metal are sometimes described as an electron plasma.
A: Pursuant to your question about permanent storage of energy, may we not say "permanent" but at least to say "indefinitely extended" storage of energy is feasible simply by vertical stacking. I believe that such contemplation of arrayed charge for either polarity is realistic whereby a negative charge upon outer limits of a galaxy produces a negative field within, and such a field invites a concentric positive domain and so on.
A: Yes. If a strong positive charge is given to a conductive sphere, according to Newton's Shell theorem the consequential outer shell of protons will present a positive field at the center of the spherical host. That field would drive protons out of the center to leave a cluster of electrons immersed within that field. 
No matter that Newton presented his theorem under his concern with gravity. Neither do I expect a society devoted to general concensus to award me with approval of this reasoning. 
The reverse polarity of my example fits atomic structure without concern for any fourth force. Electron shells thus neutralize mutual repulsion of nuclear protons. 
