Brake Stance = "Brake 1" and "Brake 2" when girl takes damage. You can set a girl to always appear to be in Brake stance

Special Crash Course = When you use the same girl for training. If you get a Crash Course you will get an extra strategies and may be other perks (extra HP or other stat. but not sure on that)

Strategies are how girl attacks. At will she will pick a target and go from there. Frontal she will go straight to the battle. From North/South she will move to the one you picked and attack from there. There are others but names give you the idea.

Popularity 4 hearts are max. At max the girls will fight better. if that means an increase in stats, or just cause she loves you i don't know.You may also get some kind of interaction with girl, that most likely means 3 star or better girls only

Divas give you a bonus. The first one you get will give + to attack %. Give them flowers till at 100% and she will sing. you gain bonus for every battle till time runs out

Mission Keys = You get 5 a day. Next time it pops up, click "Daily Mission" it will take you to a different map. You have an hr to do/redo missions on that map