Can you use a amplifier and a satellite antenna to boost a GSM signal?
Would using a typical high frequency audio amplifier that is connected to a satellite antenna boost the signal?


No, absolutely not.  In fact it would make things worse.

An audio amplifier has absolutely no capability at the (near/-) microwave frequencies used by GSM.  Quite likely it will function as a very effective attenuator and block almost all of the signal that a plain coaxial antenna cable would have let through.

Further, GSM is a bidirectional communication scheme, so an amplifier would need to have coordination or subband-specific behavior with the transmit/receiver behavior of the base radio.  Further, cellularized networks depend on the base station commanding the mobile device's power output to a level which will achieve communication, but not interfere with frequency re-use in other cells.

Such a device is not only going to be ineffective, if it were effective, it would probably not be legal.