Yes airbags will still deploy even when the seat belt is not fastened or buckled.
However when the airbag deploys and opens without you wearing the seat belt you can suffer serious injuries.
So make sure you're wearing your seat belt at all times because the seat belt protects you from getting ejected from the vehicle and protects you from serious injury from the airbag.
Also for babies that are in car seats never put a car seat in the front seat with an airbag or turn it off if possible.
Airbags activate by use of a sensor which is an electronic chip known as an accelerometer that measures the speed of the car.
When the accelerometer detects the sudden deacceleration of the car then the airbags deploy.
So when the car is traveling at a high enough speed and then suddenly stops it tells the computer to deploy the airbags.
I've had cars where the airbag even deployed when rear ended or even when I crashed into another car at a slow speed but those were old cars.
I'm not sure if it will do the same on newer cars and hope to never find out personally again.
An airbag can hurt you some if they deploy in a wreck.
However the injury and pain from the airbag is nothing when it's compared to a potential injury or even death from a car wreck without the airbag.
I was once in a wreck and when the airbag deployed from my steering wheel I got a bruise on my face and it stung for about 30 minutes.
But after 30 minute the pain and stinging went away and I was okay afterwards.
If I hadn't had the airbag deploy the injury would have probably been a lot worse.
So yes the airbag can hurt when they deploy but they can save lives as well.