Small summary of the gamespot vid of stuff I don't think we knew yet. She only got around an hour with the game and no post time-skip stuff.
-School phase is a full year of school/12 months(She stated she didn't get a sense for how long it would take you to get through the year if you do everything manually)
-New male character named Rodrigue
-There are tournaments for certain battle styles (spread throughout the year)
-Battle system is based more around combat arts (she didn't get an in depth look at it)
-They show the battle prep menu if you want to see it at around 4min
-On character's birthdays you can have a tea party for them(charm stat factors into it)
-You can hear Dedue's english voice at around 5:40
-Right after that we see the part where Linhardt is picking on Caspar's eating habits
-You can recruit characters from other houses(not sure if you can recruit more than one) if you level up certain stats e.g. Cha(charm?) and Reason to get Lorenz
-Rhea seems to teach sword, fists, reason and faith(Byleth seems to have the 3 stars next to faith)
That's about it I think. Sorry if I got anything wrong i'm getting kinda sleepy.