Miller-opamp isn't a clear technical term in my view, rather a sloppy phrase. I assume, that you mean a miller compensated two-stage OP?
1) The feedback doesn't affect the compensation directly. For the analysis, you should distinguish between amplifier open loop gain and closed loop gain.
The output load, e.g. the feedback resistor however affects the open loop gain, and to some extent the miller pole. Although a resistive load changes the open loop gain and also the pole frequency, it keeps the gain-bandwidth product in a first order.
2) I leave this simple network calculation problem to your analysis.
3) I don't understand the involved calculation. The load effect of the oscilloscope probe has to be calculated like every other load. I would mainly expect the capacitive part of the probe load affecting the OP gain. Or are you referring to DC gain? For an OP with real transistors, the output resistance is most likely below 1 Mohm.
P.S.: Rf = R1 is not unity gain mode, it's an inverting amplifier (G=-1). Both differ regarding feedback factor, unity gain (G=+1) is the more critical case for stable compensation.