I'll answer it for you.
I don't know exactly what you mean with your of question of how to use storage, but how to get more storage is to buy more crates and barrels
You don't have visible health while exploring, you have to boil water to explore more, once that runs out you can't explore. Also you have to eat food.
The death penalty is nothing sincere. When you are on a mission, and you have for example 11 skellies left to kill but you die, the mission will reset and you have to kill 20 skellies again. Nothing else will happen.