It depends on the power rating and power fed to the transmitter ultrasonic transducer. I think powerful ones are very expensive.
Why he wanted to make a such device while he could use RF?
The article says that an RF one can be detected. An ultrasonic one cannot be detected unless they knowm it is ultrasonic.
why He has used a virtual ground using an Opamp? A resistor divider could be used instead I think?
He used an LM833 dual opamp and used the second one as a virtual ground. A resistor divider and capacitor would be fine instead.
What is your idea about that output transformer?
It is a good way to step-up the signal to the transmitter's transducer.
It would not be a remote hidden microphone finally due to nonlinerity behaviuor of the air right?
The non-linearity of air occurs only when the ultrasonic beam strikes an object then the modulation and carrier frequencies intermodulate the air and make audible but very distorted sound.
This project uses a receiver to de-modulate the ultrasonic beam so there is no non-linearity.