At least if above the horizon looks dark, rising sun is dismissed.
That depends on the circumstances.
Normally the sky will be bright, but if you don't set the exposure correct, especially if you want to actually see the sun rather than just glare, it can appear dark.
Physics is fun and challenging. Anybody might find the actual physics phenomenon, at the same time they might have the wrong conclusion.
Yes, such as how you have repeatedly reached the wrong conclusion.
Even if we restrict ourselves to just focusing on how the sun appears throughout a day, with a single location on Earth; logical research would lead one to conclude that the sun goes below Earth. Either because Earth moves to put the sun below it, or by the sun moving to go below, or some combination of both.
If we go with multiple locations around Earth, then we conclude that Earth is roughly a sphere, and either it rotates on its axis to make the sun appear to rise and set, or the sun circles Earth or Earth circles the sun, or some combination.
We can rule out this nonsense idea of a FE.
So far I hold the proposition that around the middle of the year, the sun at the northen part of northern hemiplane is just the reflection of the real sun on the second dome.
And by simply noting that you cannot see the actual sun, when if Earth was flat you easily should be able to, you can rule out that nonsense (and that is even being nice and ignoring the issue of direction to it.