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Keyshon Astronomers have found the stars responsible for an explosion recorded in 1437

This nova would also have been rather low in the sky. From Seoul's latitude, the maximum altitude of the nova would have been about 7.5 degrees above the southern horizon, and not visible at all from much of Europe.

Keyshon The Neurodiversity Case for Free Speech

But it's a really bad example. In real history, Newton was able to keep quiet about views that would have gotten him fired and possibly imprisoned. Most of the "weird" Newtonian stuff the author is referring to are things Newton kept private, not stuff he published; we only know about them because of work done by historians in the 20th Century.

In particular, we know from Newton's private writings that he had strong Unitarian tendencies (that is, he doubted the validity of the Trinity). Had he made those views public, he would certainly have been fired and possibly suffered worse. (By the late 17th Century, it was illegal for Oxford or Cambridge to hire or even teach people who weren't proper Anglicans; denying the Trinity would have put Newton into this category.)

Keyshon Mass Extinction and the Structure of the Milky Way (2013)

No, in many spiral galaxies the spiral arms are present in older stars as well; that's why they're considered density waves in the stars. The contrast is stronger for younger stars, but it's there in old stars, too.

Keyshon Mass Extinction and the Structure of the Milky Way (2013)

That's an exaggerated, simple model of spiral density waves; it's not a model for the Sun's orbit, which probably only varies in radius by about 10-15%.

Keyshon A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?

Ah, I thought you were making some special argument about stars orbiting with very tilted orbits or something like that.

Yes, the orbits within the inner part of a galaxy don't follow a Keplerian curve. However, at large radii most of the visible matter is well inside the orbit and very little is outside (galaxies are quite centrally concentrated), so the rotation curve should approach the Keplerian limit as you go to larger and larger radii. The fact that it doesn't is one of the primary pieces of evidence for dark matter in galaxies (though not the only one).

(I'm not sure why you linked to that slide, since it's not calculating the field in the plane of the ring, nor is it dealing with a continuous charge distribution. Regardless, you'll note that E_x goes to 1/x^2 for x >> a, which is a "Keplerian" limit.)

Keyshon A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?

In other words, a disk-like distribution of matter does not have a uniform gravitational pull at all points of distance R from its center. You'll find it is stronger near the edge of the disk than at the same distance perpendicular to it.

But stars (and gas clouds) orbiting in a disk are essentially always "near the edge" of the disk (that is, the disk defined as matter interior to the orbit in question), so the approximation is usually pretty good.

reference to the "radial velocity" or speed of stars where I believe they are actually talking about the orbital or tangential velocity.

The (understandable!) confusion originates because "radial" and "tangential" refer, in an observational sense, to velocities along or perpendicular to the line-of-sight vector. To simplify a bit: for observations of astronomical objects, velocities along the line of sight from you to the object (detectable from Doppler shifts in its light) are "radial", while velocities perpendicular to the line of sight (which require that you wait long enough to see things change position on the sky) are "tangential". For edge-on spiral galaxies, the orbital motions that we can observe are those producing Doppler shifts along the line of sight (which are, in the frame of the galaxy, "orbital or tangential", as you suggest).

And lastly, if the dark matter obeys the same laws of gravitation, there must be a reason for its distribution to be different than the other matter.

The usual argument is that dark matter is "non-dissipative" -- that is, it can't lose orbital energy via things like radiation, the way ordinary matter in the form of gas can. (And, unlike gas, it doesn't feel pressure forces.) Stars are also non-dissipative, but stars form out of gas, so their distribution reflects the effects of dissipation in ways that dark matter can't.

Keyshon A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?

There's nothing in Newtonian theory that requires light to travel instantaneously, and Ole Romer first demonstrated that light had a finite speed in the 1670s, roughly a decade before Newton published the "Principia".