I am not a FET, but answering your question #2:

According to Flat Earth theory, the Moon distance is not actually "measured", but calculated by geometry.

On a Flat Earth world, a "pizza" disc with 20,000 km in radius, 10,000 km from Poles to Equator, anytime the Moon is right at the top of Equator, a person located at 5,000 km from the Equator (right in middle of Equator and pole, or 45° of latitude), same longitude as the Moon, will see the Moon at 45° of elevation towards Equator. By rectangle triangulation, 5000 km on ground, 45° of hypotenuse, makes 5000 km up to the Moon, that makes around 3125 miles up.

Of course, if you start to bend the ground with gravity underneath, same person will continue to see the Moon at 45° **IF** the Moon starts to go away further proportionally. If the ground bends 45° where the person is, relative to the Equator, plus the 45° of elevation the person sees the Moon, our beloved natural satellite will be pretty close to 90° of elevation to another person over the Equator seeing the "same" Moon, what puts the Moon very far away, around 380,000 km of distance in the same triangulation calculation. The same calculation can be used for the Sun. The problem is that a regular poor mortal person doesn't have a super precise instrumentation necessary to measure exactly the thousandth of a second of degree of difference when measuring at Equator or at 5000km from it, in order to get the exact distances for objects in the sky, so, on FE rounding degrees result in that 3000 miles up for the Sun and the Moon.

The same triangulation can be used to calculate the size of the Moon and Sun. As we can actually see and measure Sun and Moon diameter to be very close to half a degree, and considering FE living creatures could see them at 45° of elevation, when standing at 5000km from another person seeing it at 90° elevation, it means 111km (5000km/45°) per degree, half degree would be 55km, or roughly 34.7 miles in diameter.

So, distances and sizes based on triangulation only relies on angles of observations, if you zero all the terrain to a flat Earth, and all its inhabitants will be straight up no matter where, all the distant objects on the sky MUST be pulled close in order to keep the same elevation angle results.

If you make flat Earth concave by only 5°, all the measurements change again, the sky objects would need to be yet closer.

Two persons over the Moon in RE world, can calculate the distance to Earth, they only need to know the Moon radius, the distance among them, and the elevation angle each see Earth, a triangulation calculation will easily gives them the "h" of the isosceles triangle (if both see the Earth with exact same elevation angle number), that means distance. They can also measure the angular size of Earth, and based the distance to Earth, easily calculate Earth diameter. Knowing diameter and guessing Earth is composed of rocky material, they can also calculate volume (4.1888*r³), mass and gravity. Knowing radius of the Moon and also a rocky object, volume, mass and gravity. Earth and Moon gravity and distance gives you orbital period. Astrophysics is a fascinating field of study, not existent on flat Earth world, unfortunately.