Regarding question 1 to 3: All circuit elements are acting together, there's no thing like a "secondary resonance". You can either measure individual circuit elemnts while isolating, shorting, disconnecting etc. others, or measure the overall properties of the complete circuit
It should be noticed, that a vector network analyzer measuring complex S11, S21, S22 gives a multiple of the information a scalar transmision function can ever reveal.
Both network analyzer and spectrum analyzer have strict "external" power limits that must be observed. Measurements at a power electronic circuit in operation don't seem to make much sense as far as a characterisation of the LC circuit is intended.
By the way, the initial post is talking about RF circuits. Apparently the problem has changed somehow.