>>13928774If one of the pokemon is holding an everstone, the Nature RNG will be weighted towards having the baby's nature match the everstone parent.
If one of the pokemon is holding a training item (Like a power weight, power bracer, etc) the IV calculator will be weighted to pass a pokemon's IV of the item's stat down to the baby.
You can also control IVs by knowing exactly what IVs your parents have. Usually, each parent passes down some of their IVs at random, and others are randomized further. If you have two all 31 pokemon breed, chances are the baby will be PRETTY close to all 31.
Gender is usually 50/50, but a lot of pokemon are predominantly male (Starters, Eevees, combees)
As for Shininess, you CAN influence the RNG. If you breed two pokemon from different regions together (Say, a Jap Eevee and a USA Eevee) The shiny chance will be higher. It's still crazy small, but it's at least better. This is called the Masuda method.