I believe that you have the order of operations misunderstood.

I probably don't know that much more than you about the subject, but from what I understand, the prevailing model suggests that these Halos formed early in the formation of the universe when spacetime had varying "pockets" of density that naturally led to these halos - the formation of the galactic disk therein was actually supported by the halo existing first, because baryonic matter (aka non-dark matter, the stuff that makes up planets, stars, etc) was still too energetic from the formation of the universe to become gravitationally bound to itself.

It is attracted to the center of the galaxy.

Normal matter also makes halos or rings around the center of the galaxy. That's how gravity works. And since dark matter interacts less, it stays more spread.

All matter (stuff interacting with gravity) is attracted toward other gravitational centres, however all matter also has momentum, which may tend to carry it away from that centre. Objects don't merely fall directly toward a gravitational centre, but, subject to their initial velocity, orbit it. You may find yourself thankful for this on reflection, as the body you're likely resting on has been in such an orbit for roughly 4.5 billions of years, and will continue to be so for roughly a similar period of time.

If you're sufficiently close to the mass, and/or its radius (relative to your own and your distance from it) is large, as with, say, a stone tossed from ground level on Earth, that orbit will intersect the surface rather quickly.

At astronomical distances, ranging from some significant fraction of the distance between the Earth and Moon to interstellar and intergallactic distances, it's far more likely that an attraction will result in some other form, generally an ellipse (typical of a captured orbit), circle (a perfectly non-eccentric ellipse), a parabola (object moving at escape velocity), or hyperbola (object moving faster than escape velocity).

Ring systems form as multiple masses interact around a larger mass, be that a moon, planet, star / quasi-stellar object, galaxy, or other mass. Until the tangential velocity is lost, the particles within the ring will continue their orbit. Occasional interactions and collisions, as well as radiated energy (including gravitational radiation) may cause a given particle to spiral inwards, or be ejected from, the ring system.

<https://en.wikipedia.org/wiki/Ring_system#Formation>

I'll be straight up and tell you we have no real idea... We don't entirely know what this is. Our theory of dark matter started as "We are missing a large amount of matter in order for galaxy's to form as they do". To "We can detect this matter in rings around galaxy's that bend light, and is acted on by gravity but nothing else." and now. "We can find these pre-"historic" clumps of dark matter before they are decreted into discs".

None of this tells us what this "matter" actually is.