Gadget-2 is publicly available. Google works well to find it.
According to their website, it runs also on PCs. But don't get your hopes up, a single PC doesn't have enough computing power to simulate a whole universe. You'll need a bigger machine for that.
They have installation instructions on the webpage (see "Users Guide" under "Documentation"). You ...
That was likely the latest StarLink satellite constellation.
Note that usually it is important to give an exact time and place to answer questions like this, but in this case the answer looks fairly obvious. It really does look odd to see the constellation fly overhead (later it will disperse into separate orbits and not be very conspicuous).
There's only one kind of redshift in general relativity. The cosmological redshift, gravitational redshift, and special-relativistic redshift formulas are special cases of it, which apply to spacetimes with certain symmetries.
If you put approximate Minkowski coordinates on a patch of spacetime that's small enough to be approximately flat, you'll find that ...