With same gravity constance everything fall down at the same speed, but only in a vacuum. In an atmosphere there count the air resistance of an object, even if they are made of the same material and weight, an iron sphere of 1 kg fall faster than a iron sheet of 1 kg.

Except if you could measure exactly the speed of objects falling in a vacuum, the heavier object would appear to fall faster due to the gravitational pull on the Earth. You’re forgetting the Earth falls toward the object too.

Sad to see people trying to correct you here, maybe I can help explain.

Gravitational force between two objects is GMmr^2, for dropping objects on the Earth (or Moon) we ignore the mass of the object we’re dropping because it’s practically insignificant, but if your experiment really was perfectly accurate then the observed rate would be extremely slightly different as the heavier of the two objects being dropped is also pulling the Earth up towards it a bit more than the lighter object. If the person performing the experiment is standing on the Earth (or just using the Earth as their reference frame) they would see this as the heavier object falling faster.

R^2 is on the bottom.

That nifty gravitational law gives you the force of gravity on an object, not the acceleration. Force also equals mass times the resultant acceleration, right? So Fg1 = m1A1 = GMm1/r^2 and Fg2 = m2A2 = GMm2/r^2. m1 and m2 are present on both sides of those equations, respectively, so they cancel, and you get A1 = GM/r^2 and A2 = GM/r^2, which are identical. The mass of an object affects the force of gravity, but when you look at acceleration the mass terms cancel out.