What to use in finding frequency response : \$G(s) \cdot H(s) \$ or \$ \dfrac{G(s)}{1 + G(s) \cdot H(s)}\$?
What is the "open loop transfer function"?

To avoid misunderstandings and to be conform with the relevant literature, I like to clarify:

1) The "open loop transfer function" is the forward transfer function G(s) of the active device only without any feedback (when the loop is "open"). 

2.) The transfer function of the whole loop (but OPEN) is the so called "Loop gain" L(s)=G(s) * H(s).

3.) The transfer function of the whole circuit with feedback applied is 

A(s)=G(s)/[1+ L(s)]

Note that this formula applies for negative feedback only. Otherwise the "+" sign has to be replaced by a "-" sign.

4.) For stability analyses, we only need the loop gain response L(s) in the BODE plot (magnitude and phase separated) or in the Nyquist plot (magnitude and phase combined).