ISPR and people from the school have already explained this - there is a huge field and graveyard behind the school. They climbed with ladders, entered an auditorium and started shooting. QRF response time was good - saved many lives.
Not that massive of a security failure
The brigadier's wife - yes, that's a bit strange. How did they know about it? Did they even know or could it be a coincidence ?(not likely).
Still man. It's Peshawar; the city most affected by terror. It only took them a ladder to get in shows how much of a lapse there was. Not to mention the police check posts, that must be around.
And of course man. I don't think anyone would tell terrorists that they were some brigadier's wife in front of a gun. I bet they asked her name among all the teachers they rounded up, and singled her out for special execution.