>>35276294The only bit that is kept is gender/shininess because they're tied to the same value (The Gen I/II DVs - but the DVs themselves disappear because they don't exist anymore)
Ability is always HA, unless that Pokemon doesn't have one (the few Gen I/II Pokemon without HAs only have one ability to default to anyway)
Nature is determined by total experience, so you can force it to be certain things, see pic.
IVs are totally random, with the same overriding "3 perfect stats" we see with Legendary Pokemon.
The best way to try and get perfection (without injecting/bottlecaps) is raise experience til you have the desired nature, then clone and mass transfer the clones.