Yes. Kotaku has a good guide that's very light on spoilers https://kotaku.com/what-to-know-before-choosing-a-house-in-fire-emblem-th-1836797635
Reading now, TY.
Yes there's NG+ where you can spend a currency called renown to purchase your professor levels, weapon proficiencies, support levels and some bonus items to give buffs to people for subsequent runs
I think so. but
Black Eagle route structure spoiler
There is a splinter in the Black Eagles story (the game will clearly tell you THIS IS A BIG DEAL CHOICE). You'll want to make an extra save for those two back-to-back choices unless you wanna play black eagles twice
OK, I'll probably try to play through all three to experience all three stories then (well, 4 I guess).