Speculation on a gas giant's habitable moon in a binary system

I'm developing this story set on another planet, and would like some
feedback from people who actually know a thing or two about
astrophysics and astronomy, if this is possible and what major issues
may need to be expected.

It takes place on a moon of a gas giant which orbits a binary system.
Possibly semi-detatched if possible.
A little ancient terraforming was done to make Earth-like flora and
fauna possible.
I'm thinking of having the rotation of the moon as long as about two
Earch days, and the revolution of the moon and its planet around the
stars around 456 Earth days.
I see Titan and Ganamyde are like our moon and have rotations that
match the revolution, causing the same hemisphere to always face the
planet. Is that nearly necessary, or can I have a slight difference so
that it would appear on the moon that the planet travels around every 1
to 5 Earth years (haven't decided which yet.)

Now, if all that is possible, is it possible for the distances of the
planet from the stars and the moon from the planet, to be such that the
amount of light from the two stars would be around the same as Earth (a
little less or more is OK, the plants will have long adapted to the
change in light amount and season lengths.)
And that gravitational forces from travelling around a binary system
and around a planet, wouldn't cause constant earthquakes and tidal
waves?

(Ocassional is OK, like every few to several years. Just not whole
ecosystem destroying.)

Given the fact the tilt of the moon would be such that the planet would
appear to take 1 to 5 years to travel around the moon's sky, would it
be possible that the change in seasons could come from the distance
change over the moon's year from the stars vs. the tilt toward the
stars, and have full Earth's northern hemisphere-like seasons? (Does it
snow in Australia?)
Because I'm not good at 3-D mental imaging, but I'm thinking in order
for the planet to stay visible in the sky for anywhere from 6 months to
nearly 3 years, the moon will have to either be wobbling very slowly on
its axis, or have an odd tilt in its path around the planet, yes?

Anyway, given this, what's some thoughts on believability, how much
would need to be changed to only have to suspend disbelief only a
little, what kinds of mandatory effects on the moon would happen based
on this setup?

Thanks!
Liam