Balance Fader in Digital Amplifiers
What is the purpose of Balance / Fader in a digital Audio amplifier?

In a stereo amplifier the balance controls allows to set different gains for the left and right channel. That would be useful if the listener is not located right on on the center line between the speakers or if the acoustic loading the two speakers is very different. The balance control can be used to reposition the image in front of the listener.
A &quot;fader&quot; is more common a car. In addition to being able to balance between left and right a fader can also balance between front and rear as well. This control is mostly outdated: in a well tuned car, a fader will do more damage than good and many cars these days already have &quot;front&quot; &quot;driver&quot; &quot;rear&quot; etc. modes which are individually optimized for the use case.

In a signal flow what is the most apt position to place balance and fader(for example after before a compressor unit or at the starting of the signal flow or at the end of signal flow) and why ?

That depends a lot on what other functions the amplifiers has. It's mostly &quot;in the middle&quot;, after the &quot;flavoring&quot; controls (different modes, tone controls, dynamic loudness, dynamic range adjustments, ...) but before the speaker management (cross over, EQ, limiter, bass manager, etc.).