Although Dr. Edmond initially corrects Nolan, saying that Katrina is not a storm but a hurricane, 20mn later the same Dr tells him "Sure, stop the storm".
The baby's health parameters on the monitor can be seen during nearly the whole film. It shows the blood pressure is 120/80 and the pulse rate is 72, which are good parameters only for an average adult person. A newborn's physiological parameters for blood pressure is approximately 75/50 and the baby's pulse should be way over 100, approximately 140. Especially in this case, where the baby is considered a premature infant.
The adrenaline shot Nolan Hayes takes in the arm would have worked almost instantaneously, and not 1 minute 50'' later. That's what they're designed to do, much like an EPI pen, which is why they are so valuable in cardiac arrest patients. Further, when forced to protect his baby, he uses the drug on an intruder, with instant results. In that case, however, Hayes uses several injection pens on the intruder, who had already ingested a large amount of narcotics.
There is no electricity in the empty hospital but the snack machine works.