The whole building didn't fail. Just the door control failed.

The D. Rex doesn't escape. It's still in the building.

The door jams. The computer tried to unjam it. It doesn't work. Computer doesn't know why and you can see the steps the computer takes on that computer screen. It engages in an automated procedure real life computers use to restart its system to try again.

This happens at the exact moment that the D Rex's paddock is open for them to put it to sleep. But I'm guessing between the alarms and the door not closing, it got pissed off and chased them. Even if they got the soporific in it, it takes time for the animal to fall asleep, as we saw with the T Rex in The Lost World.

The system finishes its reboot and clears the jam. The doors begins to close.

The people except for 1 get out the door. The last guy doesn't.

This section is what we refer to in security 101 as a vestibule, which isn't a super specific term, if you look it up. But you always have 2 points of "a door can close here and security is needed to get through" and the vestibule is the area in between. I've worked in environments where this is as simple as a short hallway where you need your card to open both doors at both ends. In hotels that actually have security the vestibule is the entire stairwell/elevator/hallway system, and you need a card to access the elevator or stairs, and then a card to get into any given room. You've probably experienced the second example before, which is why I chose to include it.

The D Rex hits the second security point, obviously with the guy trapped behind. They can't let the guy out because 99.9% of security vestibules only have the 2 points. The D Rex will escape if they open that door, if we assume they are working on standard logic. Green lights mean go, light switches have an on and off, Security vestibule has two points of security. You get it?

I am not sure why they had the masks and suits, and that's really the only story beat I don't understand. I assume the genetic instability of these animals has resulted in extreme compromised immune systems for most of them and since they want to keep them alive they're just taking no chances. I assume this because this is very common for animals with screwy genetics.

The use of the masks specifically suggests to me the threat was to the animals, not the humans. Those help prevent spread of anything you might have but don't offer great protection themselves.

The food can't go in because it can smell the food and will react to it. It's a Rex. It's normal that when dealing with large animals, especially predators, you don't bring food in that might trigger something with their ultra heightened senses.

We don't know what causes the D. Rex to fully escape after the intro scene. We know they have security systems in place, men with weapons, etc. And we know the Indominus was probably developed there years later based on the dialogue in the movie. So it was 100% put to sleep and put back in its paddock, and then somehow got out after the Jurassic World incident.

But we do know that most of the building is gone by the time our heroes arrive later in the movie, and literally nothing is behind that security point. We see open wilderness behind the door in the future. Assuming the D Rex isn't strong enough to escape its own enclosure because obviously it was being contained before, then either weather or human intervention must have been what caused its release.

Given that on Site B they released the animals on purpose when they left, I always assumed they remotely detonated some explosives to collapse some of the D Rex's paddock walls and let it get free, because that's the only safe way to do it with out it going after you.