Regarding the satellite dish alignment, how can something stay in one place in the sky when everything else moves around on a 24 hour cycle?
In the heliocentric model, it's simple. Satellites orbit the Earth, each one with a a particular period mandated by the distance from the Earth. The Moon is 400,000 km away, and its period is one month (more or less). Artificial satellites are usually much closer (though more than 100 km up, that being the nominal edge of the atmosphere) and have much shorter orbital periods. With me so far?
Well, low earth orbit satellites can whip around the globe in a matter of minutes. They're really moving. The farther away they are, the longer they take to get around the Earth (both travelling farther and going slower). It's just a matter of calculation to find the orbital distance that gives you a period of 24 hours; that is, the satellite goes around the Earth in exactly the same length of time that the Earth takes to rotate (as it happens, this is about 40,000 km up). From the ground, the satellite seems to just hang overhead. Note that this can only be done in the equatorial plane, as the satellite is still tracking around the centre of Earth's gravity. Note also that Arthur C Clarke predicted the concept of geosynchronous orbits long before they put a satellite in one.
So that's how it works with a globe. My question to you is, given the proven existence of geosync satellites ... how would they stay up in a flat earth scenario? In fact, how do
any satellites stay up in a flat earth setup?