How would tidal effects behave in this setup: An icy moon orbiting a gas giant, as the gas giant orbits a red dwarf? Let me know if this is more appropriate for worldbuilding. 

Essentially, I'd like to know how tidal effects would behave in these circumstances (if it's even stable):

An icy moon orbiting a gas giant, with the gas giant orbiting a red dwarf. 

Here is a detail that may manipulate the answer:


I want the moon (if possible) to live in the red dwarf's habitable zone. It's okay if it periodically leaves the habitable zone, so long as it returns. 


I just need to know where tidal locking occurs (if at all), and how the moon receives most of it's heat (through internal heating like tidal forces or though external heating via the red dwarf).
I'm not sure exactly what your question is, but Tidal locking is fairly common for moons.   If the Gas giant was in the habitable zone of the red dwarf star, then it would need to be fairly close and as a result the Moon would need to be fairly close to the Gas giant - it should be tidally locked to the gas giant, not the star.  (A moon being tidally locked to a star is probably impossible because the planet will always have the greater tidal effect on the moon).

So your scenario, you have a moon, tidally locked to a gas giant planet, which orbits a star.   Tides don't exist in a perfectly circular tidal lock because the pressure is constant, but there's no such thing as a perfectly circular orbit, so there will always be some tidal squeezing as the moon moves around the planet.

The real question is how eccentric the Moon's orbit is around the gas giant planet, because it's eccentricity will determine it's tidal squeezing and any libration.

As far as periodic habitable zones, that would depend on how eccentric the orbit of the gas giant was around the star.  You could have it moving in and out of the habitable zone, but it would presumably be a short-period orbit, so it would be a matter of days outside, then days inside, perhaps a week or two outside and a week or two inside, unless you went highly eccentric.

All these are general points.  There's lots of variables.   

There's no one answer for where the Moon would receive most of it's heat - you'd need to work out the specifics or orbit, distance and solar temperature and then give the Moon a specific orbit and then you could work out an approximation of where more heat comes from.

and this feels like worldbuilding to me.   It's too hypothetical for astronomy.