Living on a moon with an atmosphere, how would the planet interact with the sun in the sky?

I am curious that if there were a gas giant sitting close to a red dwarf with an Earth-like satellite orbiting it:

How could we determine the way the planet appears in the sky and the way it interacts with the sun as a celestial object?
Or in other words, how does the planet in the sky appear and when would it do so given certain parameters?

I know this is a pretty complex question with a lot of things implied, but I just don't even know where to start for this stuff.

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Living on a moon with an atmosphere, how would the planet interact with the sun in the sky?

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