I can explain some things, as I rage-scienced the sharangan and byakugan last week because Kishimoto kept committing science crimes and it fueled the latest spite-researching spree.
The sharangan is the result of aliens interbreeding with humans, just like the byakugan, we can get away with fun things that the rest of the humans don't have (so long as we ignore the fact that you can't have hybridisim exist like that unless there was some serious genetic tampering from the aliens that visited so it was stable and makes Uchihas and Hyuugas a subspecies of human I guess) and we can pretend it's a dominant or co-dominant genetic trait so it doesn't die out.
The sharangan has several features-
Color changing from a very dark brown or grey that appears black to a cherry red
Dots called tomoe that appear in the iris
Swirling movement of the tomoe in the eye
Photographic memory and high processing speed
Mood swings and unstable or violent behavior (justified trait due to all canon examples shown displaying them and the talking of the whole 'curse of hatred')
Mangekyou or however you spell it
Of these features, I Cannot explain the magic. It's magic. I've personally decided dragons and electromagnetic telepathy shenanigans as my convoluted crossover explanation but it cannot be scienced away.
I also cannot find a way that the eyes would spin. It's just.... not a thing that biologically works. So you can just... not have that in whatever fan project you are doing if you want science.
Color changing can be like an octopus, little balloons of pigment that swell and contract. They can activate automatically whenever enough adrenaline hits the system and controlled however octopi do it (as science doesn't actually know from what I've read). With this they will have always been able to change the color, but we can just have the magic only work after the first adrenaline activation. Magic can tell because magic is nice like that. Don't worry about it too much. Naruto is magic ninjas. Magics gonna happen unless you alternate universe it so handwaving can work there.
With this, the color of the eyes is a very very dark red that then contracts to the cherry color when activated.
If it activated the first time with adrenaline, it should activate during all times that the body is flooded with adrenaline.
EDIT: This is something that can be done in gradients. To have a darker or brighter sharangan would be determined by the adrenaline of anger making the color be brighter than normal. Wasnt sure if that was clear enough in the above paragraph.
The next thing in order is the tomoe.
They are either extra holes, or they are color spots.
If they are color spots then it's not a big deal, just some clusters of inflated color that didn't retract with the color changing mechanism. In the hard science version, there wouldnt be power levels by the amount of dots, and there probably wouldnt be three large ones only.
Jeweling- a pattern in eyes where a bunch of small dots of darker pigment are in the iris is a Real Thing you can base it off of. Especially if you dont want the color change bit.
The hard part is when the tomoe are actual holes in the iris. If you want to use this, it would be polycoria. Which looks kind of horrific and im going to let you google that one on your own.
It usually results in being unable to dilate and undilate your eyes, blindness, double vision, etc.
This is counterproductive to what the sharangan does, so maybe don't use this one though. Unless you want to go the extra magic route and make them sense everything like Toph does (making it a byakugan recolor).
The photographic memory will have to be a thing at all times or the result of an adrenaline activation only. Then you just have all Uchiha brains wired to remember all aspects of traumatic events instead of repressing them into a blur because Alien Brain Residue or whatever.
The high processing would have to be an all the time thing or like a trauma tunnel vision thing or magic. You can't rewire your brain and back again. Either they have the same processing speed or it's all the time or it's only for the adrenaline activations or it's magic.
The mood swings and such are the result of unstable or divergent brain chemistry because they are alien hybrids. It's likely that the clan has a large problem with mental disorders on top of just plain being psychologically wired differently. This gets unpredictable and on top of the fact that most everyone with a sharangan has been traumatized to get it, it's no small wonder that they all exhibit varying degrees of mood swings, suicidal behavior, delusions, dissociation, codependency, low or dysfunctional empathy, violent episodes, and panic attacks over the course of the show.
The glowing is as said above phosphorescent bits or it's magic or a mix of both. It uses the same cues as the color changing and cannot be activated separately as just a glow on black eyes. The glowing is very faint when intentionally turned on. The adrenaline response activation would be stronger.
The glowing can be like the color sacs, but is determined by the chemicals that make up anger as well. The higher the chemicals for anger the more it glows. It cannot be consciously increased unless you are actually angry.
As chakara is canonically a thing that is connected to physical aspects, it could be a 'chakara is sensed by the glowing organs and the glowing organs then generate the glow accordingly' if you want to magic it.
I also want to add that you could do the refracting thing that cats and dogs have going on with their eyes to simulate glow if you want them to not be really obnoxiously glowy with no obvious source. Its more hard science-ey then hypothetical phosphorescent organs being crammed into an already very complicated eye.
The Mangekyou is like,,, 80% magic but you could use stress induced polycoria as it makes the user go blind and makes your iris warp. Or you could just have the extremely high levels of hormones cause the color changing bits to freak out and display different patterns. Eventually one goes blind either because the eyes got too stressed from the magic flowing through them or the polycoria making it impossible to focus and dilate correctly.
Eternal Mangekyou Sharangan wouldn't be a thing I don't think. If the eye degrades over time then all Mangekyous would degrade.
There. That's the best I've got.