Here's what I've come up with:
A main sequence star, roughly a sol analogue
Younger than Sol (say 3-3.5 billion years old)
roughly the same starting mass as Sol, but has had less time to burn off mass, so is slightly more massive than current Sol mass (1.05-ish Sol masses)
is also slightly hotter, again due to younger/more mass/burning hotter (maybe the hotter side of G2, or maybe it's a G1).
Jupiter-like elemental composition (roughly 74% hydrogen, 25% helium, 1% other, by mass)
total mass of 1.5 Jupiter masses
1.5 Jupiter Radius
I believe this mass + radius combo gives a density of about about 550kg/m^3
Semi-major axis of about 1.04 AU
I believe this semi-major axis, plus the 1.05 Sol masses of the star, yields an orbital period of about 378 days
I also believe this puts the planet within most common definitions/boundaries of habitable zones/goldilocks zones/CHZ/etc for the described star.
Rocky (metal/silicate) crust
Semi-major axis of about 4 million km
Radius of 2142 km
EDIT 4. Mass of 6.594e^23 kg (was previously listed as 6.594e^17 kg)
I believe this semi-major axis, and the mass of the parent planet, yield an orbital time of about 42 days
I also believe this radius and mass yield earth-like gravity (yes, I know this requires a core made of handwavium, or at the very least a handwaved explanation of how a core of osmium/platinum came to reside at the center of this moon...and in this manner the hand has been waved...)
No matter how I try, I can't seem to wrap my head around atmospheric retention ... I'm hoping this moon can hang on to an Earth-like atmosphere for at least a few million years, if not for the full evolutionary time range, but ... wow the info on that confuses me ...
Factors I tried to take in to account, and related links/articles/answers:
Stellar formation, stellar evolution (age/mass/temperature relationships), stellar luminosity, main sequence, Gas Giant formation/location (formed beyond frostline and migrated in later), gas giant composition, gas giant densities and radius based on those compositions(especially that if a gas giant of more than amount 2 Jupiter masses is likely to be crushed by its own gravity down to about jupiter radius, rather than increasing it's radius any more), hill spheres, formation methods of terrestrial planets, roche limits, magnetosphere and atmosphere effects on stellar winds and radiation, and the reverse effects of radiation stripping atmosphere, radiation on the moon from the gas giant planet
So my question has 2 main parts:
Is there something I should have considered, but didn't, that makes my system unstable in a time frame of a few million years (preferably a few billion), or impossible to begin with (other than the handwavium core of the moon)?
Assuming that I didn't fail to consider all applicable aspects, did I make any glaring mathematical or conceptual mistakes? (did I miss a digit or decimal, and my planet is actually inside my star? Did I entirely misunderstand a concept, like Hill Spheres or roche limits, such that even though I attempted to take them in to consideration I utterly failed to apply it properly?)