Guns don't kill people, psychopaths kill people. There should be mandatory testing for biological and genetic traits of psychopathy at the gun owners expense before a person can buy a gun. There should be a certain ratio of teachers that should carry guns. And these teachers will be tested for psychopathy in the same way, but at the school districts expense. They will also have to go to firearm lessons once a month. That is all.
Absolutely not. If anything, we can/should increase the number of trained law enforcement staff at schools (all levels) that are trained in situations that would require the use of a firearm.
Never, under ANY circumstance should a teacher have a gun. That sends so many wrong messages and puts the power of life and death in the hands of an underpaid, overworked school teacher.
The answer to the gun problem may not be easily identifiable, but it most certainly isn't arming more people that have no business being armed in the first place.