Yes, 'Solar' refers to our sun, Sol. So there is only one 'Solar' system which is our own.
I think 'star system' is acceptable as well.
I think 'star system' is acceptable as well.
We should declare terminology bankruptcy to wipe out our existing terminology/language debt, then pick sensible terms for everything. While I'm the topic, we should also do "kilogram"->"grave", "gram"->"micrograve".
Much easier than "aposelene/apocynthion/apolune", "aphelion", "apogee".
I'm not against the idea, but please don't have the new base also start with "g".
So you see, probably does not work so well.