This is where all that info came from: (What is right and what is wrong?)
LV-426 2,213 miles in diameter (3,540km) (Source is......but a very believable size for a nice large Gas Giant moon)
http://www.scified.com/topic/17394 says he copied it from Aliens Wiki?
Calpamos 117, 925 km (Not a reliable source at all, but a very believable diameter for a large Gas Giant)
https://www.pinterest.com/pin/238972323947833168/ &
http://pics-about-space.com/floating-alien-gas-giant?p=4Here it says LV-426 is only 1,200km (Highly unlikely that LV-426 is so small, from the space scenes in Alien, unless Calpamos is really small?)
http://aliens.wikia.com/wiki/LV-426 &
http://weyland.wikia.com/wiki/LV426Here it says LV-426 is 12,201km in diameter
http://avp.wikia.com/wiki/Acheron_(LV-426)And the most ridiculous one: Here it says Calpamos has a diameter of 8,800km
http://weyland.wikia.com/wiki/CalpamosI think the most important thing is to find out Calpamos's real size first...anyone know...? and it can't be more than twice the size of Jupiter, because than your in bozo science territory.
But, it might be possible for a Jupiter sized planet to have a moon the size of Earth (12,742km) as some say here
https://www.quora.com/Is-it-possible-for-an-earth-sized-planet-to-orbit-as-a-moon-around-a-gas-giant Answer 1. An iron-based planet such as the earth would be too heavy and tidal forces would break it apart. Any large moon would have to be composed of much lighter elements, such as styrophonium.
Answer 2. Maybe not. If it were not tidally locked, the tidal forces would generate a lot of heat, and melt it or even break it apart and it would never get to be tidally locked. After all the largest moon in the solar system is only 2.5% of Earth's mass, perhaps that is the reason.
Answer 3. On a Super-Jupiter or Brown Dwarf yes, (provided that your Planet is outside the radiation belt). Natural Moons of Gas Giants their mass should be less than 0.0001 of the mass of the gas Giant.
Jupiter's moons are pretty massive, but not as massive as Earth, so a Super-Jupiter would suffice. Saturn who's less massive, has less massive moons, Uranus even less.
There would be one problem, Gas Giants form out beyond the frost Zone (that we know of, we don't have gas giants closer in our Solar system for reference, but we see a lot of Hot-Jupiters though) so the moons of the Gas giants would be Water worlds if they're in the Habitable Zone of the parent star (the Gas giant can also generate heat for the moon).
A captured moon is completely plausible though. I wouldn't be surprised if Jupiter moved in and captured the rocky planets of our solar system. Fun fact: Triton is a moon caught by Neptune, so this even exists in our solar system. (Jupiter doesn't move in from perturbations of Saturn.)
Answer 4. The physics would work and it has been used a lot in Science Fiction. But as User says, moons are likely to be much smaller.
An inward-migrating giant might pick up a rocky planet as a new moon. That would probably mean a very eliptical orbit.
It's also possible that moon-formation in our solar system is not typical and that much bigger moons can form without a capture or the sort of collision that formed the Earth-Moon System.
The scietific answer: Tidal locking gives a formula for the time until tidal locking of a satellite's rotation:
tlock≈6 a6Rμmsm2p×1010 yearstlock≈6 a6Rμmsmp2×1010 years
where a is the satellite-planet distance in meters, R is the satellite's radius, the m's are the satellite and planet masses in kilograms, and μ is the satellite's rigidity, which can be roughly taken as 3×10^10 N/m^2 for rocky objects.
Plugging in Earth's radius and mass and Jupiter's mass of 1.8986e27 kg:
\frac{6\cdot 6371000 \cdot a^6 \cdot 3\times 10^{10}}{5.9736\times10^{24} \cdot 1.8986 \times 10^{27}^2}\frac{6\cdot 6371000 \cdot a^6 \cdot 3\times 10^{10}}{5.9736\times10^{24} \cdot 1.8986 \times 10^{27}^2}
5.326239e-62 (orbital radius)^6 < 1
orbital radius < 16.3028 million km
This is a distance similar to Jupiter's outer satellites.
Last answer: An author called Neil Commins answered that question is his book:
What If the Earth Had Two Moons?: And Nine Other Thought-Provoking Speculations on the Solar System.