I’m building a group of magical civilisations, in which there are seven suns, orbiting a much larger sun, each with their own planets. There are forty planets in total. Some are moons orbiting gas giants. The civilisation was built as a kind of zoo by a now departed alien race, and humans were one of a dozen alien species deposited here, so it's possible for all the worlds to have been engineered to have relatively similar gravity and year-length, compared to Earth. There’s a kind of hyperspace dimension next door which humans can burrow through to transport themselves.
I’d like to get the physics of this right, and I’m wondering what I need to take into account. So:
What factors that I’ve forgotten could potentially have made this civilisation uninhabitable for humans? What would the alien designers have needed to correct for?
How far apart would the suns need to be to avoid dragging one another out of orbit? How long would it take to communicate between them? What level of technology would you need to observe, communicate and travel between: a) worlds orbiting the same gas giant b) worlds orbiting the same sun c) worlds orbiting a co-orbiting sun
How cold would the central star need to be? Would it make sense for the inner sun to be a black hole?