Such a confusing case! I just cannot imagine why there are so few details being released, and why it seems that everyone seems to be expecting to just spot him walking around the city, with some people at the command center even telling people areas to search where he might be "hiding out". That doesn't sound like someone who is missing, right?
Also, regarding the car, it was found parked in a residential neighborhood, (not at the school) and it's my opinion that they would have had better luck just leaving it alone and seeing who returned to it. I am not sure that I understand the difference between "parked" and "abandoned". Often time family and friends can be in denial about things that a person may or may not be into. I.e. The alcohol in the car. The FIL said in a news interview that when Paul left the house he took the wife's car, not his own, which he seemed to think was at least worth mentioning. I am pretty sure he even said it was "weird".
I think there is a lot that the family is not sharing, and that's their right, but I think there is a lot more to the story. It's hard to ask the country to help find him and find finding him, but not reveal any details.
Also I am suspicious about what seems to be a huge lack of police presence. That tells me that there is not a lot of evidence that he is in danger. I hope they find him if he is in trouble, and I hope they leave him alone if he just wants to be alone.
