Yes, it is possible that with a magnetic field the moon's gravity would be sufficient to retain an atmosphere. Titan has an atmosphere denser than earth's atmosphere despite having a lower gravity than the moon. There are a few hypotheses why and one of them is that, although Titan has no magnetic field of its own, it orbits inside Saturn's magnetosphere.
https://astronomy.stackexchange.com/questions/8345/how-does-...
No, for that matter Mars doesn't have the gravity to retain an atmosphere either. I can't cite a source on this because I don't remember where I read it but I believe having a magnetic field surrounding a celestial body is a relatively minor factor in atmosphere retention compared to mass. If someone who specializes in planetary atmosphere retention knows better feel free to eviscerate me.
Titan is not only protected by Saturn's magnetic field, but it is also very cold. Some of the molecules that are gaseous on Earth are liquids on Titan. Cold gases have lower pressure, and less likelihood of bouncing a light molecule high enough up in the atmosphere that the solar wind can grab it and blow it away.
Earth has a hard time holding on to light molecules like H2 and He, but its He is replenished somewhat by alpha decay, and it takes a long time to get from the inside of a rock to the upper reaches of the atmosphere. Most of the hydrogen is attached to heavier molecules. But it happens eventually, and even the Earth's magnetic field and gravity can't keep them. Venus is almost as massive as Earth, but it is hotter than Mercury and has no core-generated magnetic field. So most of its water has already thermally dissociated (which happens slowly starting at around 800 degC) and the H, H2, He, and monoatomic O bounces high up into the atmosphere, ionizes, and blows away. So now Venus has about 90 bar of CO2 and barely any water left.
One of the terraforming proposals for Venus is to transport a large quantity of hydrogen from Jupiter to Venus, and use Fe catalyst to react it with the CO2, to get graphite C, H2O, and O2. That would strip off much of the greenhouse blanket, but the planet would still have to be cooled off and protected from the solar wind to keep all that hydrogen around on a geologic time scale.
Off topic but I’d like it quite a lot if people could be informative without being eviscerating lol. I suppose this doesn’t usually happen, but it should happen more. That’d be so much better, so much more tolerable and happier. It’d be good for all of us probably lol.
I think eviscerating comes when people present false statements as facts. Qualifying it with uncertainty as the OP did probably won't anger anybody. But telling lies because you don't know what you're talking about justifiably does.
You're pointing to an important difference: between being uninformed but trying to get towards being informed, and being uninformed but fiercely protective of your certainty.
What Would Feynman Do?
In this case, I'm imagining he'd say these are some of the things we think might explain bodies' keeping or losing atmosphere, but we have to remember that almost everything we think we know about planets and moons comes from looking at the light that bounces off of them and making guesses about the underlying rules, but we still don't know do much about the underlying rules of physics, so there's probably more that we don't know than what we do know about atmosphere retention.
