The model used for the crash sequence cost $250,000 and was so perfectly built it actually flew further than the crew and testing had predicted. In fact it flew so far it hit the camera filming it and broke the cameraman's leg.
Like James Stewart, who played Frank Towns in the original version of Der Flug des Phoenix (1965), Dennis Quaid is an experienced pilot.
The items that look like shotgun cartridges that the captain uses to start the engines are specially designed blank cartridges used in a starter known as a Coffman Starter. The expanding gases from the fired cartridge are channeled to a mechanical device that rapidly spins the engine up to start speed. They allow the engine(s) to be started without having to carry heavy starter motors and batteries, and were widely used in military aircraft in WWII, including on the Merlin engines of Supermarine Spitfires.
The production built a "Phoenix" that could be taxied, but were unable to safely build a flying version economically. Mindful of the original production which did build a "Phoenix" that could fly, but was structurally unsound and crashed killing stuntman Paul Mantz, the flying scenes were done using a radio controlled model and computer graphics.