I'm sure extraterrestrials don't speak english, so there won't be anything wrong with Sun, Moon and Solar System (which would probably just end up being Solar).
As for the calling other systems and stars by the names solar and sun, and calling all moons moon, whose to say other species don't do the same thing, say for instance, what if Alpha centaurians call our star/sun an Alpha centauri. Heh.
I suppose actually though the moon thing is the biggest problem, but if you look in sci-fi stuff the whole issue is solved by simply reverting to latin names for things in our region, including "Terra" for earth....(probably because Earthlings sounds stupid but Terrans is nice).
There are many profound and important things in life.... I just happen to think that most of them have to do with serotonin.