Are the planets and galaxies arranged in some order?

The inner planets of the Solar System have arranged themselves so that the inner Solar System is not chaotic. That is to say, the small gravitational perturbations of one planet on another do not add up to make big changes in the Solar System. That's because back in the early days of the Solar System, 5 billion years ago, things were chaotic and everthing that could go badly wrong has already done so. The result is that the spacing between planets increases as you go out, at least until to get to the outer solar system. The outer solar system evolves more slowly, and hasn't settled down yet.

Galaxies tend to gravitate onto flat "pancakes" (known as Zel'dovich pancakes after the great Russian astronomer). The pancakes tend to surround voids. At the dense places where pancakes meet, there are filaments, and where filaments meet, there are clusters. These are all the result of gravity acting on the original fluctuations in density after the Big Bang.

The plane of the Solar System is highly tilted compared to the plane of the Milky Way. The angular momentum of the Solar System must originally have been part of the random motions of interstellar clouds in the Milky Way, but the piece of the Milky Way that formed the Solar System was so small that the plane of the Solar System is just oriented by chance.

What you said about the planets is essentially correct, but the orbits are just located randomly at increasing distances from the sun, there is no pattern to it.

As far as galaxies go, they are scattered about the universe in no particular fashion or orientation relative to one another, there is no design to the universe, its just all random. The soap bubble thing is just a thought construct to try and demonstrate how the universe is expanding, it doesn't relate to any "arrangement" of galaxies. Galaxies clump together in clusters and super clusters in some regions of space but there are also vast empty voids where there is only lots and lots of nothing.

The distribution of galaxies is related to minute density variations in the plasma that formed right after the Big Bang. The best way to visualize the distribution of galaxies is to think of a handful of soap bubbles. The galaxies formed where the bubbles touch with huge voids where the insides of the bubbles are. The inflation of the universe that scientists discovered not long ago would be like the soap bubbles actually being inflated. The voids get bigger and bigger as the handful of bubbles gets bigger and bigger. You still have the same number of bubbles but they are all getting bigger.

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no

they are all just out there, no order in particular