(Assuming it’s domesticated from birth) Might an Eevee display different behaviors/talents depending on its parentage? For example, an Eevee hatchling from Espeon and Vaporeon making a good future Leafeon, or an Eevee coming from a long line of Flareon suddenly displaying pre-evolution behaviors for a Sylveon? Whatever the answer, does the same also apply to Eevee with an unevolved parent or with a non-Eevee parent, or other species with branching evolution lines like Oddish or Rockruff?

Certainly! An eevee’s preferred evolution is a conscious decision made by the eevee itself; it’s an expression of both its interests and its identity, both of which can vary vastly from those of its parents’.

Of course, if an eevee is born to a solid pack of one specific eeveelution, then they’re more likely to evolve into that eeveelution as well. This may be for two reasons: either the climate/terrain is better suited to that specific eeveelution (thus, evolution out of necessity for survival) or the eevee sees it as easier to evolve into a matching evolution so as to fit in with the rest of its pack and get along well enough to survive (thus, evolution out of social obligation … and also necessity for survival again). Thus, you’re less likely to see pre-evolutionary behaviors that don’t match the rest of an eevee’s pack, although that doesn’t necessarily mean that you will never see differing pre-evolutionary behavior.

(Incidentally, yes, the point still stands if the eevee were domesticated. Sometimes, multiple tame eevee will also form a pack of like eeveelutions in order to better withstand certain climates and areas they’re raised in. This is generally more common in regions with extreme temperatures, such as the Arctic, where eevee, even domesticated ones, will generally try to evolve into glaceon to better withstand the elements.)

If an eevee came from a pack of mixed eeveelutions, and especially if its own parents were two different evolutions themselves, it’s more likely for the eevee to pick whatever feels right to it, even if that eeveelution isn’t that of either of its parents. The same can be said for eevee whose parents consist of one eevee or eeveelution and a completely different pokémon. Because such mate pairings occur in situations where there isn’t a need to evolve into one specific eeveelution to survive (either through better socializing or simple adaptation to the environment), the eevee feel freer to explore their options and express themselves according to which eeveelution they would prefer.

As for other evolutionary families, it absolutely works in similar ways: if you have a pack or garden of solidly midday lycanroc or vileplume, hatchlings will be more likely to display pre-evolutionary behavior consistent with their group’s evolution of choice. A mixed pack, garden, herd, and so forth will yield more varied behavior.

There is only one exception to the above rule, and it’s slowpoke. A slowpoke’s pre-evolutionary behavior is that of … well, a slowpoke. They’re fascinating and wonderful creatures, but no, all slowpoke are like that, if you understand my meaning.