The airbag light flashes for around 5-7 seconds, turns off, and then doesn't come back on until the next time I start the car up. Even if the light doesn't stay on after the inital flashes, does this mean that the air bags are disabled?

 

Is this new behavior? Do you have something in the passenger seat? Is the seatbelt kept clicked in?
It is suppose to flash when starting the car as a system test.

 

This video shows exactly what the light does in mine. This is normal, correct?

 

Looks normal to me.
Blinking - arming air bag system
Light off - armed and ready to deploy

 

Yep, normal.