MacBook air shuts down abruptly while using directly with a charger, is it because I am not using battery backup?
It's quite likely to be because the battery is not providing power.
The charger's job isn't to power the computer, it's to charge the battery.
This is significant when the computer wants a lot of power for brief periods. The battery is capable of providing this short burst of full power; the charger is not, so the computer crashes.