That's a huge task, becouse it implies starting to show every single chain of logic that starts in "All is greater than Part" and "all the elements of a subset belong to the set", build from that, go through every proof to every single mathematical operation there is, up to the foundations of math itself, then go to prove how that relates to physics, until we get into the "f=g(m1*m2/d^2)" formula that explains how two masses atract themselves. So, I'll pass, becouse that would need several hundred of thousands of words. However, you can do the research yourself if you are interesting. I'll be incredibly surprised if you find any logical flaw all the way from "2>1" to Newton's Gravity Law. If you do, I'd like a small acknowledge in your Nobel Prize speechPlease, supply me the chain of logic that demonstrates with 100% certainty that an apple will fall.

If what you are asking, is an empirical proof, I'll do with just one apple and one table. If what you are asking is an empirical proof that it allways be that way, that only proves what you are asking is faulty, from a logic perspective. Becouse it's logic that "the absence of proof is not proof of absence, but the presence of proof is proof of presence". What you are asking, is a kind of logic fallacy called "inversing the burden of proof". What you are doing, is faith. It's tantamount to "you can't proof God does not exist, therefore, it does", which is faulty logic (even if God does exist. A sentence can be a fallacy, and true)
Nowhere you, or Hume, have proved that, ever. Hume is no closer to prove he is right, than Descartes is, using quite the opposite assumption.Hume isn't right because it was "written somewhere" that he was; Hume is right because of the nature of logic itself.
That's a matter of opinion. And AFAIK, the overall opinion among the philosophers, is that Kant work clearly surpased Hume (and Descartes). Hume is not the end-all of philosophy, not by a long shot.IMHO, Kant's answer to Hume was already foreseen and strongly rebutted in Hume's own work. But to each his own, I suppose.