Is it also true that the shooter started at 2am and authorities waited until 5am to arrive?
No. Again, reliable facts being hard to come by, the three hours is the interval between start and engagement/shootout with SWAT.
The shooter somehow disabled the armed guard at the door, went in shooting, was engaged by two or three other police who had happened to be nearby (I have not heard the time inter=val between start and this engagement, but it may I have been reported - I picture something on the order of 5 to 15 minutes). The armed cops spooked the shooter to go out of sight. I don't know what the armed cops who had been inside did after that. SWAT arrived, the shooter did his facebooking, calling around, shout outs, shooting some more people, etc. for another two, two and half hours (not much of that time shooting, but not none of that time shooting). SWAT, who was on scene for close to three hours, did their thing. The SWAT thing will be subject of substantial criticism on a few angles - I have no opinion. One angle is delay. Another angle is the failed explosive breach, and another angle is death by friendly fire.
The press has done its usual abysmal job of reporting simple facts.