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Both are correct, and it’s one of the trickier things to get across. I always have students work in conjunction with Periodic Table. They follow the blocks and sub levels and can see the overlap of 4s and 3d followed by 5s and 4d. Also works doe for the f levels if you venture that far out from the nucleus
It’s because we are trying to make a physical model represent the quantum mechanics of electrons. Observations tell us that Potassium begins 4s because it is an Alkali Metals. The model was never going to be perfect, so things like the overlap were developed to try and it match what we see.
Yes? 8 as the outer level, otherwise 18. Orbital filling is a challenging concept which NY mostly removed from its curriculum (they need to know electrons per level, but not the spdf sublevels). I think it is important to make it clear to students that at that level of reality, things are weird. Electrons especially are weird, and do things that would be unimaginable in our world. All of that is backed by very advanced theories and mathematics in quantum physics, but doesn't need to be understood to be successful in a HS chem class. Just know that weird stuff happens with electrons.