Is shorting and removing independent sources related to superposition theorem?
Yes.  You take the circuit as a whole and you solve for bias, using one set of approximations (Vbe = 0.6V, Hfe is constant, etc.).  Then you use the solution to that problem as inputs to the problem of finding the parameters of a linearized model (usually a hybrid-pi, but there are others), meaning in effect that you're generating a whole different set of approximations.  At that point, you have a LTI model of your system, and you can zero out any DC sources and treat all signals as perturbations around that operating point.

What allows you to do that is that you made a model of the circuit which is a LTI system.  The circuit itself isn't LTI -- but your model is, and you can play all of the LTI tricks on it to find answers.