During the plane's decent after shutting off the fuel pumps, the altimeter is shown with the hands moving counter clockwise which is normal in a descent. However, the altimeter setting (the small window on the right of the altimeter marked 29.9, 30.0, etc) is also moving. This is not an indicator, but a setting of the current barometric pressure which is set by the pilot. It would not move due to a change in altitude.
In the film the decompression of the aircraft lasts at least three minutes, and is described as an "Explosive Decompression". In reality a decompression classed as "Explosive" lasts just 0.1 SECONDS. Also a hole five feet across decompresses an aircraft in a fraction of a second.
Fighter jets are not able to track the rate of descent of a stricken target. A nearby AWACS might have alerted the controllers to the surprising response of what they presumed was the target drone, but the fighter jet pilot could not have.
The missile fired from the F-18 is an AIM-9 Sidewinder. The Sidewinder is a short-range heat-seeking missile, and would have insufficient fuel to fly 480 miles to an airborne target. The operational range of the AIM-9 is about 11 miles. As a heat-seeker, it would not rely upon radar for guidance as shown in the movie.