Can I use a gas BBQ on yomtov? And if I can how would I be able to turn it off when done?
Yes. Turn it off.
Is one similarly allowed to shut off a gas burner on Chag?
You can turn off the gas burner.
The only thing to watch out for is raising the flame not for the sake of cooking. Some flames go from “off” to “high”. You can’t raise the flame on the way to the off position. If this is an issue for you, you can blow out the flame and then turn it off.