Right, so we are the only non-sphere around. If that is the case then how do these spheres form and function? Given the fact that gravity does not function as previous thought, according to the FES. Their formation should have been impossible.
I would also be interested to find out, if we are accelerating upwards at a constant speed, why does it appear that our relative position to our neighbours does not change, nor has it changed since we first noted our position in the stars?
For the first bit, I'm not sure. We DO have 'celestial gravitation' which is essentially only celestial objects have gravity (there is a claim of difference here, but I've never been able to get to the bottom of it personally, sorry) or of course under the infinite Earth model there's not problem as gravity still exists as normal.
The primary hypotheses I'm aware of in this instance, is that either everything is moving along with us, or we've already approached so close to the speed of light, nothing is really moving in relation to us anymore due to time dilation. The first is the more popular one from my understanding however. Note that this doesn't require a dome, although some DO state this is why everything is moving together.
The entire Universe is moving in perfect synchronicity with the Earth? Come on.
The problem with every proposal of the FES is that it is all unprovable, so it is based on faith and cherry-picked science.
The fact that the Earth is a sphere is provable and has been proven, the only argument against it is that because everyone who believes it to be a lie has not been to space to observe it, or does not have the scientific training/understanding to calculate it.
Do you argue with other scientific theories because you, personally, are unable to verify them? Do you really believe that there is a global conspiracy encompassing governments, universities, corporations, scientific bodies, basically everyone and everything who could prove it, either way, is lying? You think people who go into professions where the shape of the Earth could be proven is indoctrinated as soon as they qualify?
You could prove it. Get a weather balloon and strap a GoPro and GPS tracker to it. Of course, if you did find that the Earth was a sphere, as soon as you said it was so, the FES would call you a liar and part of the conspiracy. See the problem?