Similar to the Fire Emblem games, FE: Exalted has an inventory system designed to ensure more realistic gameplay. However, it is not the same, and needs to be fully addressed.
1- Every character starts with a base inventory of 5.
1.5- Moderators and above start out with a base inventory of 6.
2- Unless otherwise stated, all items by default take up one inventory space.
3- If your inventory is full, you will not be able to receive new items. It is possible to swap out new items for existing ones, though...
4- While some consumable items maintain multiple uses, they are not stackable.
4.5- On that note, neither are weapons.
5- Every 5 levels, you gain one inventory space. If you use a Second Seal and switch to a lower-level class, you will lose your bonus inventory spaces as well.
Any other questions pertaining to the inventory system can be asked here.