Interbreeding is common. It's one way to pull a hidden trait out. For each trait (fur, eyes, tail, ears, whisker), there is one shown trait and one hidden trait that each cat has. The more dominant of the shown/hidden traits is the one that shows on the cat. For example, your teacup shows a mysterious tail. That means the hidden tail trait is either mysterious or one of the more recessive traits. There are charts on recessiveness that can help you target what you are trying to show on your next kitty.
Fabao's chart shows dominance of tails, ears, whiskers
https://docs.google.com/spreadsheets/d/1TrDVn0kBF3NhtJewvP4pjq5bYYOrLC10Sk_VyYIWQTc/edit#gid=0
Saga's charts on fur dominance
https://docs.google.com/spreadsheets/d/1Gb6Kv82bO_5owi7VdDCstIxl-yS0ebfjbqOqM_-LApU/edit#gid=0
Saga's charts on eyes dominance
https://docs.google.com/spreadsheets/d/1Es6gKInU8_D906PJZLARIK9sc-GfVAYNCGxU9nixvgE/edit#gid=0
Saga's folks also do a blog
http://sagakitty.blogspot.ca/
As to who establishes dominance, everybody contributes charts to help establish dominance. It is a community effort to find out the dominance of traits whenever Kittycats releases new traits.