I just wanted to reach out and answer this question and give you a little bit of feedback. First of all, there is a LOT going on in this question. The line “I would like to understand all of chemistry” is particularly distressing, and I’m tempted to say “wouldn’t we all like that!” It is often a very good practice to try to narrow your questions down to a manageable extent so that answers can be direct and to the point. It is no fun if someone has to guess what question they should be focused on!
On a more serious note, the questions you are asking are all fundamental questions in the subject of physical chemistry, particularly the sub field of quantum chemistry. The fundamentals of quantum mechanics are often treated in a junior or senior physical chemistry course, and there are several good textbooks for learning about this subject as well as some online resources. I am personally drawn to Donald McQuarrie’s “Physical Chemistry: A Molecular Approach” and Claude Conen-Tannoudhi’s “Quantum Mechanics” (a bit heavier on the math and physics side). If you pick up those books and dig in, you will find answers to these questions and countless others. Otherwise, I recommend looking online for resources such as MIT’s open source lecture materials https://ocw.mit.edu/courses/5-61-physical-chemistry-fall-2017/ or Andrei Tokmakoff’s lectures and notes online (University of Chicago, though these are likely better for more advanced studies) https://tdqms.uchicago.edu/.
As far as a direct answer to some of your queries about electrons, let me give a brief sketch of an answer that you can follow down the rabbit hole. The wave function is not the same as the potential energy. The potential energy is a part of the total energy, or “Hamiltonian” operator. The Schrodinger equation relates the Hamiltonian operator to the wave function and allows you to solve for the quantum mechanical states via the eigenfunctions of the Hamiltonian. So, if you change the potential, you change the wave functions. The orbital shapes you describe are precisely the spatial graph of what those wave functions look like after you have solved the Schrodinger equation either exactly or numerically (or at least the pictures show the real part or square of the wavefunction). Now, the nature of the interactions of two electrons is simply given by Coulomb’s law. This is also, unfortunately, the piece of the potential energy which makes it so incredibly difficult to solve for the orbitals of molecules! If you want a VERY in-depth discussion of this issue, the Dover book “Modern Quantum Chemistry” by Szabo and Ostlund is the standard. But suffice to say that the electrons are absolutely interacting with one another, and this gives rise to all of the chemistry that we can observe. In fact, it so precisely the complexity of the electron’s interactions with each other that makes chemistry so complex, and the nuclei are often treated as “fixed charges.” It is exciting that the field of computer science is now robust enough that we can compute some of these electronic properties with basic web-browser based technology like WebMO https://www.webmo.net/. If you would like to run your own test calculations, there are examples on the website.
I hope that this assorted and scattered answer is useful to you. You’ve opened up a can of worms into a giant and exciting mix of fields here, and I hope I’ve left enough to pique your interest without scaring you off.
