I think the important question here is how different do you feel things would be if our sun and moon were to act like Equestria's.

Not so much that they're controlled and revolve around Earth, but that they work in such a way that night always has the moon, and day always has the sun.

While typing this, I realised that this means the moon would have to constantly be on the opposite side of Earth and would have to move somewhat random without any real structure to it, which also means that it won't have the force of revolving around Earth in order to not crash into it...

But we're talking hypothetical.

Surely life can't happen with this...

It was discussed (among many other things) in this thread:
https://www.fimfiction.net/group/20/human-in-equestria/thread/351784/full-analysis-of-equestria-canon

TL;DR - The moon would always be full, and (unless the sun was slightly off-center, forming an angle between the sun/earth/moon) in a permanent lunar eclipse. This would, in turn, always make the moon have a reddish tinge due to Rayleigh scattering of all the blue light through the planet's atmosphere (same as how sunset/sunrise works).

This would also mean that the moon has the exact same rotational speed as the Earth, and doesn't have any gravitational attraction to the planet (which would cause it to, as you say, rotate around the planet and disrupt the premise of this thought experiment). In short, the only way this could actually work out is if the system were somehow geocentric rather than heliocentric, as then both bodies would be revolving around the planet, allowing for gravitational influences while retaining the other stuff.

One of the stories in my favorite section is about Zecora and some stuff she deals with. She talked about how during Nightmare Moon, the sun was over her tribe/town (and the whole nation) for days and the crops died. Ever since they hated or were afraid of the sun.

The moon would be revolving much slower than it does currently, at a 12th (approximately) of it's current rate, only completing a revolution once a year. The centrifugal force that keeps it in a stable orbit wouldn't be as strong, and would cause it to eventually collide with earth, and wipe out all life on the planet. Think Armageddon, but with a much bigger object hitting us, so much so that it would most likely actually cause both bodies to catastrophically fracture, and eventually reform as either one bigger body, or 2 bodies in some sort of orbit, repeating the cycle until a stable orbit can be established, which would be something mimicking our current state. The tides would be noticeably affected as well, though you would still have 2 cycles a day like we do now, but instead of being at different times each day, gradually shifting back and forth over the course of a year (not taking into account the higher tides you get when the moon is directly in line with the sun) high tide would always be at noon and midnight, while low tide would always be at 6 in the morning and evening. I can't be sure about that, I'd have to think on that affect for a bit. It would be in permanent lunar eclipse, and always a full moon.

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........you are very knowledgeable on this subject hmmm? I’m very impressed by your reasoning! I didn’t even consider some of things you did, nor did I actually look at a calculator.

I'm just really good at visualizing stuff like that in my head.

The 'moon wanders off' explanation is somewhat wrong.
https://en.wikipedia.org/wiki/Lagrangian_point - L2 is somewhat stable.
The pull of the earth on a body outside the earth and sun adds to the suns gravity, decreasing the orbital period.
At one location, L2, this gives you a period of one year.
L2 is about 1.5 million km out from earth.
The moon would need to be some three times its current diameter - around that of earth - to look the same, and would be around a million km from earth, as the comparable masses change the distance as the new moon would pull on the earth, changing its orbit.

This is a quasi-stable situation, and could persist for long periods with very minor maintainance.

The GAIA space telescope is at L2.