Evolution, revolution or imagination? Off the top of my head, all three in stages as needed. It would be revolutionary as it evolves from one stage of progress or failure to another with a touch of imagination to keep it from going stale or, again, as needed. The parts would individually duplicate the whole, and the whole would duplicate the individual parts down to the last part.

1) The government would hopefully be a true democracy, not representative democracy.
2) By the democratic process of votes.
3) We’d have to discuss and vote on that.
4) I would think at first, the govt would be funded by Earth for exploration and living alternatives, and probably exploited for anything Earth could use via natural resources or scientific advancements.
5) My concerns about my govt would depend on circumstances once in place but overreach tends to be my biggest concern.
6) Hopefully the same ethos as the star ship Enterprise, in a perfect world. To see new life and new civilizations, pure exploring without interference. The Prime Directive.
In all reality, knowing humans, it would probably end up as conquering.
7) At first there would be limits, as we explore natural resources and work out a system. After that I would think that over time, there would be few limits as everyone should have equal opportunities to change their lives for the better. Perhaps background and criminal checks so we don’t get killers and hardened re-offenders there.

A democracy, like here in the US. There might have to be some changes, as with terms and length thereof, but, basically, the same.

I would base it on the US Constitution. However I would add a clause that congress needs to be voted in every 4 to 8 years as well, instead of life time appointments.

@Dutchess_III Yes!