Can you create a powerful magnetic field out of confined circulating electrons only? Would it be possible, regardless of how efficient it was to do something like this, or why you would actually do it, to generate a really powerful magnetic field simply by producing a cycling electric current with lots and lots of electrons, without any actual physical medium like a superconductor material that you would normally run the current through? I know that this sounds similar to particle accelerators and/or superconductors, but that isn't quite what I am imagining.
If you were out in near-vacuum of space and you could set up a loop where electrons whipped around very quickly, most likely under the influence of an external magnetic field that directed this, would the electrons on their own be able to generate a magnetic field, or would you need a magnet or a core material, as in an electromagnet, to activate or amplify the magnetic field somehow?
If you were able to collect enough electrons to be equivalent to say, the mass of the Earth, and you had a very large energy source, like the Sun, or a neutron star, that emitted a powerful enough magnetic field that you could somehow attenuate or direct, could you create a very powerful magnetic field that way?
 A: 
If you were out in near-vacuum of space and you could set up a loop where electrons whipped around very quickly, most likely under the influence of an external magnetic field that directed this, would the electrons on their own be able to generate a magnetic field, or would you need a magnet or a core material, as in an electromagnet, to activate or amplify the magnetic field somehow?

Italics mine.
The electrons  can be in  a circular orbit due to a magnetic field which has to be continuously supplied. 
The well known Bq/v=mv^2/r trajectory.
Their orbit cannot be self sustained. The minute the external field is stopped the electrons will follow a straight line.
As pointed out in the comments electrons can be manipulated in a medium , which is how electromagnets work.
Self sustained magnetic fields exist in plasmas, called magnetic cosmic plasmas. because they have been observed in the interstellar space and are studied in models of the sun.  It is a whole field of study and research as one discovers by a search on the net.
A: Any current (flow of charges) produces a magnetic field, ragardless of if it is in a medium or not.
$$\oint \vec B \cdot d \vec s = \mu_0 I$$
where $\vec B$ is the magnetic field and $I$ is the current. If the electrons are flying in a straight line, the magnetic field will be concentric circles around the current, like this:

At any point in space, you therefore have a magnetic field that is perpendicular to the current flow.
To get a field similar to a bar magnet, you need a loop, and as you said already, without a conductor, you need a magnetic field to deflect the electrons.
That said, you can of course amplify the magnetic field by using an iron core for example. This basically just changes the value of $\mu_0$ to $\mu_r \mu_0$ and you end up with a stronger magnetic field. However, there still is a magnetic field even without that core ($\mu_0 \neq 0$).
About the question of the neutron star...I'm not sure why you would want to take the detour with the electrons if you say that object creates a magnetic field anyway. Also, consider that static magnetic fields drop with $\frac{1}{r}$ from a source.
