TL;DR: the "Stars" wiki page and the "Universal Acceleration" wiki page seem to contradict eachother on the presence/absence of gravity. If gravity does affect the things "orbiting" earth, why does the earth itself (supposedly much larger than any other objects in the flat earth model) not succumb to gravity and collapse into a sphere? If the earth is not affected by gravity and there is, in fact, no such thing, why do other, (supposedly) smaller things orbit around each other?

I am not a flat-earther, but I was interested in how believers in the flat earth model explained constellations and how they vary hemispherically (yes, I did find the wiki page on "shifting constellations"; this is not a question about how constellations work). I know how wildly the details of flat earth theory can differ depending on who you ask, so I figured that if I wanted a theory accepted by at least more than one person, I'd find a source that came from the aggregated contributions of multiple people. I knew that tfes.org is relatively active, so I visited the wiki and checked out the page on stars: https://web.archive.org/web/20190506203543/https://wiki.tfes.org/Stars (link preserved via wayback machine because wikis can be edited).

The page itself is well thought-out, I will give whoever wrote it that, but it is based entirely on the assumption that gravity exists and affects objects on a large scale.

Each star in a cluster is attracted to one another through gravitational vectors. Formation is created through gravitational capture - at least three objects are actually required, as conservation of energy rules out a single gravitating body capturing another.

Emphasis mine.

After reading, I wondered if the "Stars" page was not the multi-contributor theory I had been curious about, and perhaps was instead just the fleshed out theory of one individual, because the commonly accepted flat earth model rejects the existence of gravity (at least as it pertains to Earth), as shown by the wiki page on universal acceleration: https://web.archive.org/web/20190506210026/https://wiki.tfes.org/Universal_Acceleration

Universal Acceleration (UA) is a theory of gravity in the Flat Earth Model. UA asserts that the Earth is accelerating 'upward' at a constant rate of 9.8m/s^2.

This produces the effect commonly referred to as "gravity".

The traditional theory of gravitation (e.g. Newton's Law of Universal Gravitation, General Theory of Relativity, etc) is incompatible with the Flat Earth Model because it requires a large, spherical mass pulling objects uniformly toward its center.

Emphasis mine.

Although, I noticed that the definition of gravity refuted here does not specifically mention gravity as it relates to non-Earth objects (perhaps because there is no widely accepted theory about the wider "universe" of flat earth theory?). A quick google gave a convenient definition of gravity that does include how it pertains to things that are not Earth:

grav·i·ty
/ˈɡravədē/
noun
1. the force that attracts a body toward the center of the earth, or toward any other physical body having mass.

So, my questions are:
Why would gravity apply to objects like the stars orbiting the earth, but not the earth itself? Why does the earth have any sort of special exception from a force that governs the behaviour of many other things orbiting around it? Unless the Earth is "special" or "different" in some way, would it not experience the same attraction towards a center of gravity (which would eventually lead to collapse into a sphere) that the stars do towards the supposed central point above earth they orbit?

I don't expect answers using high-level physics to mathematically prove the flat earth model--I unfortunately would probably not be able to understand them even if someone did choose to do such a thing, because I have not yet finished high school and have a limited understanding of mathematical processes that fall outside of algebra. Also, any answers including explanations that rely on the claim that god(s) exist(s) will likely fail at convincing me, as I have yet to encounter proof of god(s) and thus do not believe in them.

Thanks in advance.