I assume from your FAQ that you are generally familiar with both special and general relativity. I assume that you believe that we are not living in a gravitational field, but in fact an accelerated reference frame. I understand the Equivalence Principle very well. Locally, you cannot do any physical experiment to test the difference between an accelerated reference frame or a gravitational field. However, over large regions you definitely can tell a difference. If the entire earth were an accelerated reference frame, the gravitational field would not vary at all. It wouldn't vary across the surface of the earth, and it wouldn't vary with height. I am a physicist, and I have tested both of these things experimentally. The gravitational field varies across the surface of the earth, due to the different densities of material beneath. The more dramatic field change is that it varies with height. It seems to me that you are also denying that gravity exists at all, which means you are denying the second half of general relativity which explains how mass-energy distorts space-time.
There are also experiments you can do to prove that the earth is spinning. There are measurable Coriolis and Centrifugal forces that change with latitude. These affect projectile motion and are essential in calculating such things as missile trajectories. The direction and magnitude of the measured forces are perfectly consistent with a body the shape of an oblate spheroid rotating about a central axis with a period of one rotation every 24 hours.
I'm not sure if you are denying gravitational affects or not, but don't forget that it is completely possible to measure the gravitational "force" between two masses in a laboratory. I know this, I have done it myself. It's a fairly sophisticated procedure, but it can be done.
The easiest test of geometry would be to measure the circumference and radius of a circle that is confined to the surface of the earth. We should measure the distance around the earth at the equator (circumference), and the radius from the equator to the north pole (radius). If the circumference is exactly 2pi (6.28 . . .) times the radius, we are living on a flat earth. If the circumference is closer to 4 times the radius, we are living on what is close to a spherically shaped earth. If you want to prove to the world that you are correct, you should do this experiment. I would recommend flying in an airplane around the equator at a constant speed and measuring the time it takes to circle it once. Then I would fly from the equator to the North Pole and time that at a constant speed. Does it take 1/4 or 1/6 the amount of time. I'm guessing that it takes you longer to get to the North Pole than you think it would.