Back to the original topic, I immediately see many flaws in this theory.
1. How would satellites work?
2. How do you explain the other planets?
3. How did all of this come to be in the first place?
4. Why can we not see this sphere?
5. If the sphere was constantly rotating at a rate that would give us enough force to remain on the earth, airplanes would easily be overtaken by the rotation of the sphere.
I'm sure someone will post a ridiculous answer to all of these, but it was worth a try. 
Firstly let me say that I don't know if I accept this model yet, but it is very interesting and I have been researching something similar recently, but haven't reached any conclusions as yet. Nevertheless some of these points apply to standard FET so I will attempt to explain them:
1. They don't. They don't work in standard FET either, the signals we receive are from broadcasting towers or high altitude aircraft. The FAQ has more on this issue if you are interested.
2. I can't answer on behalf of the OP, but in my personal view the other planets move about the sky just like the sun. Their motions are explained by the Ptolemaic epiycle model.
3. Who can say? In RET we don't know what caused the big bang, nor can we know. It was the beginning of the universe as we know it and we can't conclude anything about what was before it, or even
if there was a "before it". I don't believe any FE model has yet explained the origin of the universe, just as RET hasn't. Sure, we have the big bang model which explains how the universe came to be as a result of essentially a giant explosion of energy and matter (though the formation of our universe after this is not without some theoretical problems, but that can be discussed another time). RET cannot explain what caused this explosion which formed the universe, just as FET does not explain the origin of the universe.
4. Again, I cannot answer on behalf of the OP but in my research into the issue I was leaning toward what is called in physics a perfect black body, it absorbs all electromagnetic radiation falling on it an therefore appears as pure black despite having the sun and stars to illuminate it. Actually the perfect examples from physics class practically never find their way into real life, but it wouldn't need to be strictly perfect, a close approximation would do. Perhaps it reflects / radiates a small amount of energy back, this would explain the cosmic microwave background nicely.
5. Straightforwardly false I'm afraid. The rotation of the sphere in this model is at such a speed as to account for gravity by centripetal acceleration, planes would fly the same way in this model as they do in the standard FE model, which is the same way as they fly in RET. There is always some confusion over this issue when gravity and UA are brought up in threads, people just need to remember the equivalence principal. Essentially, gravity causes things to accelerate towards the earth, UA and the centripetal force proposed here cause the earth to accelerate towards those things instead, but the effects, to an observer here on earth, are the same. Think of filling a bucket with water and swinging it over your head rapidly. The water does not fall out because centripetal force keeps it in. If you left the bucket on the ground, the water would not fall out because the centripetal force keeps it in. The result is the same either way because the forces are equivalent despite having different causes. In this model, a plane flying would be traveling
with the earth and would therefore experience the same centripetal acceleration. Just like in RET when a plane takes off, the earth does not suddenly disappear out from underneath it despite the earth rapidly traveling around the sun.