Question about extra inventory for bag.
Bag slots you buy only appear for that character. If you want extra bag slots for another character you have to buy them again. Price in the BLC is a bit steep I think for a slot per character.
Extra bag in inventory is unlocked by gems only for that character.
Extra slots in bank is unlocked by gems and can be accessed by all characters.
In short, if you want to unlock slots on a character’s inventory, be sure you won’t delete that character any time soon.