Say if a houngan used a spirit to possess his van, for the Movement power and armour boost...

1. If another spirit tried to use the Search power on someone in the van, would it count as the target being behind a ward?
2. What if someone dual-natured wanted to try to enter/exit the van? Use the ward mechanics again?

No, and no. The van would become dual natured, not the inside of it. If someone was astrally projecting, and tried to stick their head in through the door, then they couldn't. But it wouldn't protect from search, or from people going in and out of the van.