Hello!
Have you modified your encounter after already starting a session with your family? If yes it means that "active session" is now separate from the campaign you was preparing. "Prepare" mode is the mode where you set up campaign before you run it with players. Once campaign started it creates a copy instance for players and doesn't fetch changes from "prepared" campaign. This is done so you could start same campaign for different parties without having changes intersect between each other.
About possession. During combat GM can possess an encounter, it means if you try to possess anyone from active combat, you will get everyone under your control. You can switch back to game master mode but creature will still be under your control, waiting for you unless you will manually select "Give control to AI".
(+/-) are controlling the level of the encounter, i.e. every creature in it.
AI options sets beahaviour of the NPC when its controlled by AI. It controls the decisions npc will take based on the current combat situations. Ranged AI for example will try to get higher ground as fast as possible. Berserk will go for its target no matter what.
You may want to take a look on the tutorial video and take a look on the "The Hungry Journey" campaign that give some hints and basic overview:
https://www.youtube.com/watch?v=ZSh7hOZl9hg
