My question is to the Flatearthers is, what is the mechanics that reproduce this observation on a Flatearth?
As much as I feel dirty for saying this, I have to agree with totallackey. This is
long, easily one of the most complicated parts of a model, and it's hardly worth reproducing the full explanation, especially on a site like this where a lot of the time it just plain isn't going to be read.
If you are genuinely interested in an answer, then great, but equally someone genuinely interested in an answer will be someone willing to put in the effort to understand. If that's the case, my sig links to a full outline of my model. It has to be gone through in order; four sections (though just the first three build up to this). They're lengthy, but pretty much all of that is necessary background for the answers to your questions.
After all, FET is a ground-up new model to RET. RET takes a while to fully explain orbits, and most of it only feels simple because you're used to it. Going through gravity, how that can lead to 'endless falling,' applying that to multiple entities, for starters... It's nothing simple. Ditto for FET/DET.
So, from this point on in the post I'll assume you have a working knowledge of DET from the overview, and the FAQ. I agree with the spirit of most of your observations, though there are a few details I take issue with, though again, all explicit in the model.
The observation of Mercury and Venus, are seemed very close to sunrise or sunset.
Morning observation of Mercury and Venus end with sunrise as they are washed out by the suns glare.
At sunset, thy are loss as thy fall below the horizon. With a telescope you can see that there are phases like of the Moon.
The observation of the Moon is different then other observations, as its sizes is close to that of the Sun, it rises in the east and sets in the west, but it moves further east, each day, taking about 29 days to get back to where was, and can be seen during the mid day. And the moon goes through phases from a full moon, to new Moon (all dark).
The moon-related questions are explained in the overview. As Mercury and Venus are similar entities, they will have similar properties, and further will be washed out by the Sun's glare, as you say. The tilt of the Earth governs how various celestial objects will appear to be in different locations at different times.
With the other planets, them are seen in the the dark of night rising in the east and setting in the west during one night. As you plot the outer planets from one night to next thy do not stay in place with the background stars, this motion is call retrograde motion. It was this observation, that change the earth centered Solar system, to the sun centered Solar system. I can go through the mechanics of it, but I will hold off.
To be fair, retrograde motion was previously explained by means of epicycles for a geocentric system. The reason this wasn't satisfactory was simply the lack of a good mechanism. On DET though, for starters I hope you'd see how planets would never be expected to stay in place with the stars.
The degree of the Earth's tilt varies. The whirlpools have a 'focus,' and there are many above the Earth. As each of them line up, or move apart, you get completely different behavior, repeating in only the long term. The tilt, however, essentially makes the planets look as though they're reversing direction as our sight of them shifts to be viewed from a new perspective. When the tilt is in line with a planet, that's when the retrograde motion occurs. Repeating, predictable, but only on large timescales. This essentially gives an analogue to epicycles, only with an explicable mechanism.