Answers to
1.) Phase margin is defined for the loop gain only. Of course, stability properties have an influence on closed-loop peaking. However, we cannot quantify the margin in this case.
Exception: For a second-order circuit we can find a relation between (positive) phase margin and the amount of peaking as well as overshooot (step response).
2.) For measuring/simulating the loop gain we must open the loop and inject an AC test signal. Condition: Same DC operating point and same load conditions at the opening as under closed-loop conditions. Therefore, no extra test DC voltage allowed.
Comment: The DC operating ponz remains unchanged because the test signal source is connected BETWEEN both nodes of the opening (and NOT between loop input and ground).
3.) See 2)
4.) In principle - yes. However, under the mentioned constraints (see 2) it makes sense to find a node for breaking the loop where a low output resistance meets a high input resistance (Opamp case: opamp output or high-impedance input). Only in this case, we must not use an "artificial" additional load to restore the closed-loop load conditions.
5.) When you want to qualify the stability properties: No, the test must be performed for the loop open (loop gain). If you need the information "stable or not stable" it is sufficient to analyze the closed-loop operation.
6.) For finding the loop gain we must measure the signal strength at the output of the loop (at the opening) as a function of the test signal only.
Therefore, no other input signal allowed.
