Is it possible to operate BC548 npn transistor in Active region using single 9Vdc battery?
This is what you have in the second image, drawn more appropriately, and without the short.







simulate this circuit &ndash; Schematic created using CircuitLab

Because the base of the transistor is tied to the 9V rail, the emitter can never be less than a diode drop, the base emitter junction, below 9V. As such the collector can never be less than that. That only leaves under 0.6V across the LED and it's resistor.

You need to wire it like this.







simulate this circuit