Question: For a fantasy, I need to know how a world similar to Earth would exist in a geocentric model. 

1) I would assume the sun would have to be a lot smaller. I'm okay with artificial stars (hand-wave that stuff away with magic). But I would like to know if that makes an Earth-similar planet impossible. (I don't need other planets in this model.) For example, how would it effect... 

* seasons and climate
* length of day, month, or year
* sunrises and sunsets
* gravity
* constellations and/or navigation
* any huge effect I don't have enough science to anticipate

2) How would I manipulate my universe's model to make it more Earth similar if those things are completely off? It doesn't have to be exact, but I need a temperate climate with pretty normal seasons and climate zones.

Answer: 
The first thing we must understand is that from a purely *kinematic* point of view, the heliocentric and geocentric models are both equally correct within the accuracy limits of astronomical instruments available before the, say, 16th century. There was no way for an astronomer who lived before [Tycho Brahe](https://en.wikipedia.org/wiki/Tycho_Brahe) to bring serious arguments in favor of one or the other. (That's why Galileo Galilei had such trouble with the astronomical establishment of the day -- he simply did not have any good arguments to bring in favor of his pet theory.)

The problem is that from a *dynamic* point of view, for a geocentric model to be correct it is necessary to abolish the law of universal gravitation: and this means, of course, that the universe in which a geocentric model is correct from a physical point of view has vastly different physics from ours. Whether *"a world similar to Earth would exist"* in an universe with vastly different physics than ours is not something that anybody but you can answer.

How would it effect...

* Seasons and climate:

We don't know. The law of universal gravity doesn't work in your world, so we have no idea how wind works, how the water cycle works, the lot. By the way, how does *fire* work in a world where the law of universal gravity does not operate?
* Length of day, month, or year:

Those are purely kinematic phenomena, and from a purely kinematic point of view the heliocentric and geocentric models are both equally correct within the accuracy limits of astronomical instruments available before the Renaissance.
* Sunrises and sunsets:

The sun will rise and the sun will set. We have no idea how the atmosphere works, or how thick it is, because the law of universal gravitation doesn't work in that world. So we don't know if, for example, the sun will appear red at sunset.
* Gravity:

*Our* kind of gravity doesn't work in an universe where the geocentric model is correct. It must be some different force which is called gravity. How it works nobody but you, the author, can say.
* Constellations and/or navigation:

No effect whatsoever. The funny thing is that *up to this day* celestial navigation, as an application of practical astronomy, is done assuming a geocentric model. See [celestial sphere](https://en.wikipedia.org/wiki/Celestial_sphere) for how this works.

Of course, satellite-based navigation systems won't work, because the law of universal gravitation doesn't work.
* Any huge effect I don't have enough science to anticipate:

The main huge effect is that only the author can say how that world works, because it most definitely it doesn't work like ours. What keeps water in the ocean, what keeps people on the ground? Does hot air rise? Why? Are there tides? Why?

Note that you *do not* have to make Sun any smaller or bigger -- whether we adopt a heliocentric or geocentric system has no impact on the distance between the Earth and the Sun.

Everything also applies for the Moon. A Moon may or may not exist; if it exists, it is not universal gravitation which makes it orbit. What is it that keeps the Moon in orbit only the author can decide.
You don't have to change much at all, if you don't force yourself to follow Newtonian mechanics to explain planetary motions.

For one, universal gravitation was not mainstream until Newton built his system around it. Until then, it seemed possible that other heavenly bodies might not exert any kind of gravity at all. If you use this approach, then you don't have to worry about the size of these other bodies, or what they might do to your Earth (Although you might want to give the moon gravitational pull if you want tides).

People also once theorized that the other heavenly bodies moved in fixed tracks around the Earth; if you are willing to assert that some divine being fixed a track (perfect circles, for instance), then you can make them go wherever you want, as fast as you want, and you don't have to give a scientific justification for it.

If you're doing fantasy, there's no reason you should feel committed to being Newtonian about everything. Heavenly bodies were once thought to follow different laws than earthly ones; you could make that a reality in your world. This would also give you a lot of freedom to shape them as you like.