for some reason the third act (like after the metropolis) when I descend to the mission, there are two models of the ship and the alien herself, and after I go to metropolis again, everything is black but the game is still ok for some reason
Yeah, that's a bug I'm gonna have patched out in the next version. Levels weren't meant to be revisited, but I made some mistakes in that endeavor.
You need to talk to Theremin and make the choice to either head back to Diadem XII or collect the probes before trying to head back. The former option should make the world map inaccessible, and the latter should allow you to proceed to the final mission. And then AFTER the final mission, there's another bug for trying to go back to the world map again.
Sorry for the inconvenience!