Yes, there are 14 challenges, for every combination of ship ant Tier - 4+3+4+3.

If it doesn't specifically say "base XP" - it can be boosted. So yes, it does

Armory is persistent, so it doesn't reroll, you can even acess it witout entering the game. https://armory.worldofwarships.com

Aren't Colbert and Ohio new?

It in the container description: