Since your User name is TheEngineer, I assume you have some knowledge of engineering?
I would like to think so.
Well, in FE (or RE) will an object "fall" the same rate in a vacuum?
Yes.
If it does, then I can prove that there is an attraction between Masses (which we call gravity)
I would love for you to prove that to me.
according to the theory that Masses exert a force of attraction between them
There is your problem.
Ok, TheEngineer. Let me state again:
As you agree objects in a vacuum fall at the same rate. So, if the same object is dropped repeatedly, will it always fall at the same rate unless there is something that can influence it?
If this object is electrically neutral, non magnetic (and is shielded from these influences) and varies it fall rate in direct proportion with the Mass around it, then is it logical to conclude that it is the Mass that is effecting the fall rate of the object?
Well, this is how the Gravimeters work. They pull a Retro reflector up to the top of a tube that has had the air extracted from it (a near vacuum), then drop it and measure the rate of fall. These are so accurate that they can measure variations in the fall rate around one thousandth of one billionth in fall rate.
They have placed large masses above these machines and measured their effects. Mass really does have an influence on the fall rate of the retro reflector. Therefore there is something that Mass produces that is not of the other forces (Not Electromagnetic, not Strong Nuclear and Not Weak Nuclear forces). The only other force is Gravity, which is the attractive force between two masses. As this is exactly what is occurring, then the only conclusion is that gravity really does exist and at the strengths it is claimed to be.
If gravity exists, and it exists at the strength that it is claimed to exist with, then the Earth can not be flat, but must be Round because if it was flat, then the attractive force between the mass of the particles of the Earth would cause it to collapse into a ball. SO even if it did start out flat, it must now be round.