A few comments on your star system.
One) It is unknown whether a moon is important for life on a planet. Since Earth does have a large moon making large tides and providing bright light, Earth life has adapted to the tides and to the moonlight in some nights. And there is speculation about whether having a large moon was necessary for life to begin and flourish on Earth. Nobody really knowns how important moons are for planetary habitability.
Two) The moon will orbit the planet, and thus it will sometimes be on the same side of the planet as the star or stars. When the moon is not visible from the night side of the planet, it will be unable to reflect light from the star(s) back onto the planet, just as the Moon is not always available to light the night on Earth.
Many persons have asked on this site for methods to give a planet a moon which will always be in the same position relative to the planet and the star, and they have always been told that was impossible because the moon has to orbit around the planet.
Three) An irregular moon will not be large and massive enough for its gravity to pull it's materials into a rounded shape. Thus it will be considerably smaller than Earth's Moon, and it will have to be only a fraction as far from the planet as Earth's moon is, if it is to be about as bright as seen from the planet.
Four) A planet can exist in a star system with three or more stars, up to perhaps a maximum of 7 or 8 stars in a stable system, but a planet can probably have no more than two suns. I define a sun as a star which provides a significant percentage of a planet's light and heat and which is close enough to have a visible disc as seen from the planet.
Planets known to exist in binary star systems either:
- Orbit one star, with the other star much farther away, in a S-Type or noncircumbinary orbit.
- Orbit both the stars, in a P-type or circumbinary orbit.
In a triple star system, two of the stars would probably orbit each other, and the third star would be more distant. For reasons of orbital stability, the distance between the third star and the pair of stars must be at least a few times (and sometimes hudnreds or thousnds of times) as large as the distance between the two stars in the pair. And a planet orbiting around all three stars would have to orbit several times as far as the widest orbit of any of the stars, in order to have a stable orbit.
So that all adds up. or multiplies up. to a considerable distance between the planet and the stars, if the planet orbits around all three stars and all the orbits are stable. And at such a distance, the planet is unlikely to be warm enough for liquid water using life.
And in fact, I don't know of any planet in any multiple star system which orbits around more than one or two of the stars.
Five) A planet can not have the right temperature for liquid water using life if it gets too much or too little radiation from its star or stars. So a habitable planet has to orbit with a fairly constant distance between it and all of the stars in the system that it gets significant amounts of radiation from. So the only stars which a habitable planet can get signficantly closer to or farther from have to be stars that it reeives minor and insignificent amounts of head and light from, so that variations in the amounts it receives from them are not important.
Six) A planet has to orbit at the right distance from the star which serves as its sun (or the two stars serving as its suns) to receive the right amount of radiation from that star(s) according to the type of star.
Stars have spectral classifications and luminosity classifications. Habitable planets can only orbit main sequence stars, which are luminosity class V, and only some spectral types of them. This has been known since scientists worked out the life cycles of stars in about the 1940s.
Every star has a circumstellar habitable zone where a planet would receive the correct amount of radiation to have liquid surface water.
So it would seem simple to calculate the inner and outer edges of a star's circumstellar habitable zone by comparing the luminosity of the star to that of the Sun and mutliplying rd dividing the size of the Sun's habitable zone.
But as you can see at:
There are many widely different calculations and estimates of the Sun's circumstellar habitable zone.
To be safe a writer could always put a fictional planet as the distance from its star where it receives exactly as much radiation from its star as Earth gets from the Sun. I call that the Earth Equivalent Distance or EED.
An answer by user177107 to this question:
has a table listing the properties of various classes of stars, including their EEDs where a planet would receive exactly as much radiation from its star as Earth gets from the Sun.
So it is comparatively easy to find the EED of one of the star types listed in that table, and put a planet at that distacne for a star of that type, and know you have the planet in an orbit certain to be in the star's circumstellar habitable zone. But if there are two or more stars in the system, it is harder to arange the orbits correctly.
Seven) You have system where a red dwarf star and a class A main sequence star orbit a class G main sequence star.
Actually the less massive stars would orbit around the more massive stars.
A red dwarf would be a spectral class M star of the luminosity class V. The table at: https://en.wikipedia.org/wiki/Red_dwarf shows that their masses vary from about 0.7 the mass of the Sun for an M0V to 0.08 of the mass of the Sun for an M9V.
Spectral class A main sequence stars vary in mass from 1.62 times the mass of the Sun for an A9V to 2.4 times the mass of the sun for a spectral type A0V.
So the combined mass of the red dwarf and the class A star would be between 1.7 times the mass of the Sun and 3.1 times the mass of the Sun.
Main sequence class G stars vary in mass from 0.9 times the mass of the Sun for a G9V star to 1.06 times the mass of the Sun for a G0v Star.
So the combined mass of the red dwarf and the A class star would between 1.603 and 3.444 times the mass of the type G star. So the G type star would orbit around the red dwarf and class A pair instead of vice versa.
Eight) There is a book discussing the requirements for a planet to be habitable for humans. Habitable Planets for Man, Stephen H. Dole, 1964.
To make a long discussion short, Dole decides that a planet has to exist with a fairly constant level of radiation from its star for billions of years after forming before it can produce an oxygen rich atmosphere suitable for humans - and lifeforms with similar requirements - to breath.
STars only shine with a fairly steady luminosity during the main sequence stage of their existence. And the more massive a star is the quicker it will use up its hydrogen fuel and end the main sequence phase of its existence.
Dole calculated that a star has to be no more massive than 1.4 times the mass of the Sun to be on the main sequence long enough for one of its planets to become habitable. That corresponds to a F0V or F2V star, less massive than a spectral class A star.
So if there is a spectral class A star in the system the system and the pplanetsin it can't be old enough to have a planet habitable for humans or for lifeforms with similar requirements.
Unless, of course an advanced civilization terraformed the planet to make it habitable.