This explanation flies in the face of Newton's Laws, so I suspect you think those are fake as well.

Not really, newton is just very badly misunderstood (due to intentional miseducation to make him an idol). Gravitation is not newton's idea, and he specifically asked that his name not be associated with it because of how stupid and philosophically unsound it was. You can read about it in his own pen if you wish.

Taking for granted that weight is a constant

Well, it is and it isn't. It is constant (or at least primarily constant in stable substances/atomic structures) in regards to intrinsic weight (weight without buoyant force), and varying in effective weight (weight with buoyant force factored in).

does everything fall to earth at the same rate in a vaccume?

Excellent question, and a splendid place to begin.

Firstly, it is worth understanding that a vacuum is not an attainable thing in reality. You cannot devoid any area in existence of all matter - it cannot be done, even theoretically. Nature abhors a vacuum. So we are discussing partial vacuums only (i.e. chambers that still have, at least, gas filling them)

In partial vacuums, archimedes law (and drag) still applies. The answer to your question, is NO. Only things that are the exact same density and shape could possibly fall exactly the same way (probably for TOTAL exact, you'd need the volume to match too...) Of course, functionally the difference is so slight that our "rule of thumb" is typically adequate for use.

If so, how much does the earth weigh

No one has any idea how much the world weighs, obviously.

and why doesn't fall beneath our feet?

Ah, the famous "out of phase" paradox. What keeps them from just falling through the floor now that they are "out of phase"?!

In science we try and explain phenomenon that ARE, not that you think OUGHT to be. Leave the scifi fanboy snark for hassling capt kirk (i.e. nitpicking fiction).

We don't imagine phenomenon that aren't and then contrive fiction for why it ISN'T (not in f*ing science anyway).

The world doesn't fall beneath our feet. So we have no need to explain why it should. Does this make sense to you?

All of the matter is stacked on all the other matter. What is at the bottom you ask? Why it is turtles, all the way down - naturally. When you ask stupid questions, get ready for stupid answers!

Is there an infinite ground below us?

No one knows. The deepest we have ever drilled is around 8 miles. We haven't the foggiest what is down there, and anyone who says otherwise is deluded or lying.

If that's the case, how is it possible for one to traverse all continents and end up in the exact same place by heading in a single direction long enough?

Technically/pedantically, it isn't. Essentially no one can go in a single direction for an entire trip (even around their house, let alone the entire f*ing world). It isn't possible, and it isn't verifiable/validateable because of the challenges of motion through the world.

Now let's actually address your question in earnest. Circumnavigation is a large circle over a large plane (possibly bowl or other shape, but essentially certainly not spherical). You pass over the continents when they are beneath you, and you end up where you started when you complete the circle. No, you cannot fly over the south pole in order to get to the north one on the other side. In fact, there may be no (singular) south pole at all.

Ama!