1) Did we discover planets gravitating around Alpha Centauri A ?

 

For instant no, but in 2012 we discovered a gas giant gravitating around Alpha Centauri B. After verifications we saw that it was an measurement error. However it is possible to discover planets in this system.

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2) A moon gravitates around a planet, which gravitates around a star. So its distances to the star are varying a lot, but can it still have a stable surface temperature ?

 

Yes, that's possible but these variations will depend of the distance between the moon and the planet, the type of planet, the atmosphere of the moon...for exemple some of the moons of Jupiter are constantly frozen and keep a stable temperature.

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3) Have we discovered planets with materials which are superconductor at ambient temperature ?

 

Not already, because just a very little exoplanets have been observed to the naker eye. In fact we discover it mostly by very slight bright deviations that tell us that a mass is present at a certain place around a star. So we cannot observe the colour ar study the ground of the planet or even study its atmosphere by spectral analysis.

 

 

Now, we know by a reliable source that it is possible for a planet to gravitate around Alpha Centauri A. Furthermore, if this hypothetic planet is a gas giant (which is the case of Polyphemus in the movie) and if it has ideal caracteristics (good distances etc...) it could allow the existence of an habitable moon (our hypothesis concerning the retention of the temperature through the greenhouse effect is confirmed by Sophie). However, detect it by naker eye might be impossible, and we couldn't know its composition (except by building very powerful telescope, using new technologies like spacial interferometry...).