I'm writing a science fiction story set on a moon orbiting a gas giant. I want to understand how the world's day night cycle would appear from its surface and how the world might be affected by this particular orbit. 

For the purposes of the story the world needs to be as Earth-like as possible. It is primarily tropical and is one of several moons orbiting the gas giant. The gas giant at times fills most of the moon's sky and at other times is absent. Also I'm assuming that on some nights the gas giant would appear lit up at night, like a much larger more luminous version of our moon.

I've assumed that the world will sometimes be cast into darkness as its view of its star is blocked by the gas giant. At other times a specific area on the world will be in darkness because it is facing away from the star (like Earth does) despite not being blocked by the gas giant. 

Would this give the world two different types of night? How long would its days be? Would it have days or nights of varying lengths depending on where in the lunar cycle it was?

I'm also assuming that the world spins on its axis (in order to generate the required magnetosphere).

Although not strictly hard sci-fi, I'm looking for a way to frame this world's orbit that is plausible and also naturally occurring. I'm not looking for heavily maths based answers as I just need enough detail to frame the story, and physics is not my strong point. 

Cheers for any help you can give.