Dimensions, mathematics!?!

There are things in quantum physics that kind of defy our sensibilities like particles pop in and out of existence. Energy/Matter you know ;). Particles are able to be entangled with one another. A particle can be at 2 different positions at the same time. Schrödinger. Particles can be in front of a barrier and can spontaneously pop out on the other side of the barrier. Because of the probability, quantum tunneling. All of this is just mysterious. Let me ask you, lets suppose you‘ve got a sphere and I live in a 2-Dimensional universe. And you now take the hollow Sphere and let it fall through my 2-Dimensional world. How will I describe this crazy spooky phenomena. Well in first case i will see just a dot, then a circle, which gets bigger and bigger until its reaches its maximum, the middle part and then gets slowly smaller till in the end its a dot and then nothing. If you might image sitting somewhere in your flatness and out of nowhere you see this. You might freak out because its not really explainable for you. But for someone from the higher dimension, where you are actually able to see that, that is a sphere passing through the 2D world. It would be like nothing special aint it ?
So who is there to say, that the most mysterious phenomena which we describing accurately, but dont make sense at all, make sense in a higher dimension. But now, i want to totally blow your minds if im even able to, but you should be with me on this one.
A point has no dimensions at all, no height width or length. A line has 1 dimension, a length. A square has got 2 dimensions, a length and a width. A cube has got 3 dimensions, a length, width and height. Ok ? Follow me now.
A line is a 1 dimensional structure with 2 zero dimensional points, got it. A square is a 2 dimensional structure with four 1 dimensional sides, right ?!? A cube is a 3 Dimensional structure with six, 2 dimensional sides aint it like that.
So right now, we‘re going up by the boundaries. No 1 dimensional line without 2 points, no 2 dimensional square without 4 lines, no 3 dimensional square without 6 sides. We go from 2,4,6 ... and each side is one dimension less. So now lets think, if there are some things we‘re not able to explain in our 3 ways. What if there must be some sort of 4 Dimensional cube, which should have atleast 8 some sort of sides and every side of this, must be a 3 Dimensional cube. So if you might be in a higher Dimension, the sides must be 3 Dimensional cubes, where we actually live in ... But what does that mean to be in a higher dimensions, now image you being in a sort of middle ‚4D cube‘ and by all your possible 8 sites there are normal cubes. What would you be able to see, dont mind but thats just my fantasy but if you live in 3 Dimensions youre able to move yourself or anything in 6 ways. Up down, left right, front and back. And ofcourse we live through another dimension, its the time which we are passing trough thats the 7 th way. Why shouldnt you be able to move in 8 ways. That sounds kinda crazy but image seing back in time by looking left, and then when you look on the right youre able to see ‚future‘. Or to look at this whole structure from the above. As you might now understand, there is a keypoint my brain which evolved since the beginning of the life on our planet. Is not actually able to make me or myself think about this kind of topics. Its the mathematics which we invented or found?
Picture is taken from the tesseract wikipedia page.