When it says all bodies must be in storage. Does it mean the everybody on the map must be put in a container or all bodies you make via knocking out or killing must be put in a container? The 1st place guy kills people and puts them in containers. Can i beat the whole game then bag and hide all bodies?

fill every container, if you cant then store everybody you can, as per the rules

So I must fill all containers

if you can, as per the rules