I've read this question What would the periodic table of a 4-Dimensional universe look like?, and I think it answers part of my question about how atomic physics would work, but I'm not sure. Would a 2-dimensional atom have any rotational axis? How would that affect the spin? How many orbitals would be in each energy level? I'm assuming that protons, neutrons, and electrons exist.
I moved this over to Physics. https://physics.stackexchange.com/questions/449678/what-would-the-periodic-table-look-like-in-2-dimensions