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: 
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.
Assuming that Newtonian mechanics still apply the factor that determines whether the Earth goes around the Sun or the Sun around the Earth is the mass of the sun. If the sun radiates equally in all directions then its total power output must be proportional to its distance from the Earth.

Assuming that the mass of the Sun is small compared to that of the Earth, an orbital period of 30Ms (about 1 year) gives a radius of about 2Gm corresponding to a sphere with a surface area of about 5.5E19 m^2. For a power density of 1.361 W/m^2 the Sun must produce 7.4E22 W. If it burns at this rate for about one billion years then it will consume about 2.5E22 kg of matter. For comparison, the mass of the Earth is about 6E24 kg, so if you postulate a light-weight machine with a store of fuel which it converts to energy and radiates in all directions then this arrangement could be plausible.

However, if you have a machine converting fuel to sunlight then why assume that it will waste most of it? If it could focus its entire output on the Earth then it could reduce its power consumption by a factor of about 430,000 and at the same time make the mechanism more easily accessible for the maintenance crew.

Unfortunately the radiation pressure would push the Sun away from the Earth, so perhaps it should radiate an equal amount in the opposite direction. This would produce as a biproduct an interesting galactic lighthouse.

From the perspective of a fairly primitive civilisation this should be almost indistinguishable from a heliocentric system. Weather would be similar, although I am not sure what effect the absence of the Sun's magnetic field would have. If you want a moon like Earth's then you must make arrangements to illuminate it. Maybe spread the beam in the plane of the Moon's orbit, or even provide a separately focused beam. Comets would be interesting, as they would now be orbiting the Earth rather than the sun, and they would abruptly disappear as the passed out of the beam.