If Einstein was in an elevator in free-fall in a vacuum and in his upturned hand was a miniature elevator containing a miniature Einstein who had a miniature elevator in his hand and so on in ever decreasing sizes until the last elevator is on the scale of the Planck length would all these objects theoretically fall at the same rate?
The answer is no, these objects would not "fall at the same rate," because all the Einsteins' masses would attract each other. All Einsteins would be accelerating toward their barycenter, and thus would fall at different rates with respect to any reference point, such as the ground they're falling towards or the barycenter of all the Einsteins.
Mass of an object is an intrinsic property of the object itself, independent of the gravitational field.
Weight of the object depends on how it is moving and it has direction. Objects in freefall are weightless.
The answer to your question is yes, all the objects would be in freefall and feel weightless independent of their sizes.
In a roughly uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body roughly equally, which results in the sensation of weightlessness, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity). The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.
Not at all. Einstein elevator makes zero the acceleration, not the velocity. Fortunately, Einstein elevator lead us to a uniform aceleration. So we don’t need to deal with position and speed uncertainties
We only have plane waves moving down ar several speeds. Of course, Elevators might not remain in Alberts hand for so much time: smallers ones will be the first changing its relative position due to the well defined z position. No body said velocity were the same for all of them at anytime.
The gravity here is emergent not only from the body they are falling towards but also each other. They will fall on different paths due to the relative masses. The force of gravitational attraction is the same so the speed of movement in the vacuum is the same but they will not fall towards the massive body at the same rate. Individual objects on tiny scale may have some own motion so they are not in inertial frame. Answer is no. No objects will fall at same rate.