Some basic questions about effective field theory (EFT)

In summary, effective field theory (EFT) is a theoretical framework used in physics to study complex systems by focusing on low energy phenomena and taking into account the hierarchy of energy scales. EFT differs from traditional field theory in its ability to simplify complex systems and incorporate new information, but it has limitations in its applicability to high energy phenomena and its ability to make precise predictions. EFT is used in various practical applications, including particle physics, nuclear physics, condensed matter physics, cosmology, and astrophysics.
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Elmo
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TL;DR Summary
Concerning the operator product expansion and the expansion of the heavy propagator
I had been studying this topic from various textbooks and review articles and I am confused about some terminologies and concepts. The question I have typed in this PDF.

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