On the meaning of distinguishability, and wavefunctions for 3 electron atoms
The only case in which electrons can be considered distinguishable is when they are so well separated that their wave functions do not overlap. Any electrons on the same atom or within the same molecule are considered indistinguishable. 

In chemistry we like to talk about electrons being in specific orbitals, but the indisinguishable nature of them means that they are all in all orbitals simultaneously. This is why a mathematically rigorous description of a molecule using hybrid orbitals is just as valid as one using canonical orbitals. Neither is true in the sense of describing where each electron is, and both are true in the sense of describing the collective electron density.