I don't get all the resistance to putting a cop in schools

[BarackTheVote]

193. 1. Not necessarily, and if they break in, alarms would go off

alerting security to the exact attempted point of ingress, so that it can be avoided.
2 & 3. I think they'd have a good chance, and I definitely think they'd be able to get a call off and hunker down, buying vital time.
4, 5, 6, & 8. Not talking about stair wells, I'm talking about fire escapes. Most casualties in evacuations come from large volumes of people using very few routes. Increase the routes, decrease the amount of people using each route and decrease the time it will take to evacuate; additionally. In the Columbine instance you brought up, their strategy wouldn't work at all, because the evacuees would not be using halls or high traffic areas, they would not be corralled toward the gunman, because there's no way a gunman could cover a hundred different escape routes.
7. Intruders could still break in, and because, in this world, there's no security officer to take action, they'd have all the time in the world to break in, and once in, that class is dead, period.