As someone who is curious about this way of thought, I was looking into the Q&A. I found two things that seem to contradict each other, and while I'm hoping I'm just misunderstanding, I really would like to know.
In the section, "How do you explain day/night cycles and seasons?" you give this great gif showing how the sun moves to give us different times of the day. You can see it here
https://wiki.tfes.org/File:SunAnimation.gif. The gif brings the idea that the earth is staying still while the sun moves around us.
In the section, "Why doesn't gravity pull the earth into a spherical shape?", It mentions this, "The earth is constantly accelerating up at a rate of 32 feet per second squared (or 9.8 meters per second squared). This constant acceleration causes what you think of as gravity." This quote brings out the idea that the earth is spinning, while the first one suggested differently.
If I am misunderstanding this please inform me of what is actually going on. While I am not sold completely on the flat earth, the moon landing is fake.