This question is pretty straightforward:

What is the minimum and maximum distance for a planet to be in the habitable zone of an average sized (not biggest, not smallest) Red Dwarf star?

There is no consensus now if such thing as habitable zone really truly exist around red dwarfs.

Flares

Most red dwarfs flare, doubling their luminosity in matter of minutes. This shifts zone with optimal temperature very much, very fast, and planet may be in it, and literally five minutes later be outside of it.

Flares also tend do throw a lot of charged particles and do funny things with magnetic field. If any planet around red dwarf is able to keep atmosphere is still an open debate.

Tidal lock

Red dwarfs are cold. This means that "habitable zone" would make planets orbit their stars so close they would get tidally locked. Tidally locked planet would have its star-facing side above the temperatures needed for life as we know it, and space-acing side much colder. This would create strong winds, except your planet does not have atmosphere due to flares anyway.

There are other minor issues, but these two points are biggest, and easiest to explain reasons why talking about habitable zone on context of red dwarfs in general is moot. It is only reasonably possible to talk about habitability of a specific planet orbiting specific, probably exceptional, non-flaring red dwarf.

Searching for circumstellar habitable zone lands you on this wiki page

In astronomy and astrobiology, the circumstellar habitable zone (CHZ), or simply the habitable zone, is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure. The bounds of the CHZ are based on Earth's position in the Solar System and the amount of radiant energy it receives from the Sun. Due to the importance of liquid water to Earth's biosphere, the nature of the CHZ and the objects within it may be instrumental in determining the scope and distribution of Earth-like extraterrestrial life and intelligence.

The habitable zone is also called the Goldilocks zone, a metaphor of the children's fairy tale of "Goldilocks and the Three Bears", in which a little girl chooses from sets of three items, ignoring the ones that are too extreme (large or small, hot or cold, etc.), and settling on the one in the middle, which is "just right".

The same page also contains the following explicative picture:

Image By Chester Harman CC BY-SA 4.0

What is the minimum and maximum distance for a planet to be in the
habitable zone of an average sized (not biggest, not smallest) Red
Dwarf star?

Flattening out all sudden magnetic and luminous flux variations (assuming the author has a way of achieving this by Sci-Fi means or just "Atypical Stability of the System"):

• For the mean luminosity of an "average sized red dwarf" (in this case Median size - about 0.15 of the mass of the sun):




• The habitable zone would extend between 0.04 and 0.1 astronomical units (Distance of Earth from Sun) with the closest to Earth's level of illuminance being at about 0.055 AUs.

As you can square on this diagram: http://sites.psu.edu/ceh5286/wp-content/uploads/sites/4579/2014/04/ndistance_HZ_09022014.jpg (The image is free to use but too massive to upload to this site.)