Electronic – output impedance seen by the inductor

Concerning the fact that Q dropped when you used an impedance matching network:

You used a simple L matching network consisting of just two components (a capacitor and an inductance) which both are completely determined by the input and output impedance of your situation.
This leaves you no parameter to control Q. You get whatever Q is a result of the component values you need for matching.

So I suppose what you need is a more sophisticated matching network containing at least three components (e.g. a T- or a Pi-network) that has another degree of freedom which allows you to control not only input and output impedance but also Q.

Since you are also asking for references I recommend very much the chapter about impedance matching and Smith charts in Chris Bowick, "RF Circuit Design". It explains and contains an example problem for impedance matching while also caring about Q.

You misunderstood the "axiom"

An Ideal opamp will do what it can to make the differential voltage between the -ve pin and the +ve pin equal zero. It doesn't state it is zero

All it can do is alter its output and thus with negative feedback there OPAMP stands a chance of making the difference zero

You then make use of that fact during circuit analysis to simplify calculations "if the difference is zero and the +ve terminal is at 0V, then the output must be...)