I don’t think there’s all that much to imagine. Jupiter and Saturn both have moons heated by tidal forces, including Io, Titan and Europa. “Heated” in this sense still means really freakin’ cold (especially at the surface), but better than nothing. The key is that you still have substances moving around between the core and the surface. You may or may not have an atmosphere, and the thickness and composition clearly vary even in our own solar system. If you went swimming, it would probably be liquid methane or ammonia; liquid water would only be underground. Volcanoes would not be molten rock, but might have things as hot as liquid water (which would immediately freeze).
It would be dark all the time, like a moonless night on Earth. You’d only be able to see the planet you orbited because it would block out stars behind it (like a new moon on earth). You would not have weather-related seasons like we do on Earth.
It would depend entirely on where they’re observing us from, and what methods they’re using to detect planets.
If there’s a Kepler-like spacecraft launched by a civilization living on one of the Kepler planets, and it’s pointed at a region of the sky that includes our sun, they’d be able to find us without much trouble. Well, they’d at least know that there’s a solar system containing eight planets, one of which is in the habitable zone - assuming they define “habitable” in roughly the same way we do.
Actually I understand our galaxy is believed to have collided with and consumed multiple “dwarf galaxies”. For example, skimming Wikipedia (this thread got me going on the astronomical articles there), I see that the Sagittarius dwarf elliptical galaxy is believed to be in the process of being absorbed by the Milky Way, and the Omega Centauri globular cluster is suspected to be the remnant of a long-consumed dwarf galaxy.
Sorry, they would not. The Kepler mission is looking at a single region which is not in the ecliptic (so as to avoid the Sun shining into the CCD and blinding the spacecraft). A Kepler-type mission around another star would have to be very close to our ecliptic to detect planets here.
