1. Do external doors start with a closed door token and so all entrances require an ap to open(either chop wall or open door)?
External doors are always 'open' with no token initially (or ever).
Of course, you could always house-rule a hardcore mode to have all external doors closed at game start. Or even have a random chance for internal doors to be open (1-2 on d6)... Or use the locked doors from one of the Kickstarters in play... Etc Etc
2. Do false leads count toward the POI goal? The rule book says to place them in your saved victims area which sounds like the count but a false lead not being a save feels like it shouldn't count
No they don't count towards the POI goal.
We actually placed 'discovered' ones in the 'Saved' area, and 'killed' blank POI's in the Dead area, just for posterity (and to keep track of how many blank POIs have been accounted for. This way if you lose, but your 'Saved' pile has a mass of blank POIs, you can feel slightly better about your loss... I dread games where the first 4 POI's are all blanks...