A bit more specifics to Hana's Tomboy skill if the wording wasn't clear. It deals damage to units surrounding her, not the ones adjacent to the enemy she defeats.
I saw a 4x crit damage from hamayama's stream (25 -> 100) for one of the clubs so maybe that's the new higher crit damage mechanic for Killing Edge/Killer Lance.
Stores have to get the shipments beforehand so they can prepare the display/promotion. Smaller shops may be able to break street date without much repercussion but larger ones usually can't afford to get blacklisted. Downloads are controlled by the e-shop so this applies to physical copies only.
It looks like there's a Buddy Seal for A+ (A only for Kamui) supports and a Marriage Seal for S supports. These let you reclass to the partner's class. Once you're past the required level, you learn a skill every level up. Parallel Seal gives you a few choices rather than becoming the partner's class.
edit: The part I couldn't quite understand was the bit about promoted classes can learn unpromoted classes' skills. Do they assume you went through the same promotion path as your partnet and give you those skills too?
You can probably go by the stats but I'm seeing promoted (上級職) for both Kamui and Ryouma while Sakura, Kazahana, Camilla, Marx, and Joker are all base classes (下級職).
I think Sakura's personal skill is more like reduce damage by 2 rather than a factor of 2. And the (つえーつえー) at the end could be describing it as really strong.