Yes,there is no way to create empire with people who do not want that.And muslim,hindu,China,Russia,Germany,Izrael and USA would certainly do not want it.
Japan and South Korea - maybe,maybe not.
So,i would divide world into 4 categories :
1.want join my empire.Moste african and South America would go for that.Central Europe,too.Poland would be covered becouse i am from Poland.Full economical and military support,they get better military when they could defend it.
2.Those which do not join,but i could rescpect them and they are not enemy of my state,Poland or catholic church - could go into cosmos with lesser technologies,defended from space from 3 and 4 categories.For example,Japan.
3.Do not attacked me,but are hostile to my state,Poland or catholic religion - for example Birma.Do not let into cosmos,but trade what i made.
4.Hostile and attacked my state - destroy their military and satellites,do not let build any again.Not trading anything.
Good I like how you thought it up.
1. There are a few who will join up, it may take some time and it does depend on how much autonomy the states have. For example Hungary, while they are patriotic they may be willing to leave the EU for the goodies you have. They'd acknowledge you as leader of this alliance and would be willing to join as long as they get autonomy within there own borders. What would you call this alliance/empire the holy league?
2. Japan would want to ally with you simply because of the Gundams lol. The Gundam franchise is like there star wars, they also don't have any historical beef with Poland unlike Germany and Russia. Though in the past they did ban Christianity, now it is a legal religion, though most Japanese aren't Christian.
3. I'm not up to date with the most recent news but does modern day Burma oppress Christians? I know it's in east Asia so they can't be aggressive to European nations. But I do know nations like China, and North Korea oppress Christians.
4. Makes sense you don't want to let your enemies build up, and eventually destroy you.
So what would you call your nation, would it have a diffrent name than Earth Poland? Also would you try and get a Catholic priest on your space station to be recognized as a cardinal so you could maybe later try and get in installed as Pope, when the next Papal election happens?
Looking at the original OP, you are the only human being on the station and far from being omnipotent.
Which means it's going to be difficult, because I would need to recruit people in order to run anything but the most basic functions. Thus I would need to bluff the heads of states that would be calling warnings, while trying to contact people i know from real life or internet, which I would then pick up in a shuttle, so I could form nucleus of HR/security service which will handle the immigration, so I can build a functioning society, instead of just a clique of gay nazi bodybuilders internet shitposters.
Work up deals with some nations to allow migration, instead of daring shuttle escapes of the chosen few, counterintelligence would have to work hard to limit the spy infiltration. I could probably trade rejuvenation treatments to rich and influential assholes, for various favors in this regard. Otherwise I wouldn't get involved in planetary business too much, technology superiority only goes so far and resentment at borderline alien interference could be a powerful unifying factor. Thus I would get involved in only the most onerous cases, otherwise I would focus on exploration and exploitation of the wider Solar system.
You know if I remember correctly in Elysium didden't one of the people have some information uploaded, or downloaded into his brain? Couldn't this be used to download the memories of anyone you are thinking of being a citizen and then having an AI look over them to see if they are a spy? Though yes not getting involved in earth would be less likely to burn you.
Now that I think about it, it would be incredibly difficult to prevent spies onboard the colony from communicating with other nations outside the colony. They wouldn't even need to use radio signals (which can be jammed/intercepted/decoded/traced/etc): if there is a window onboard the colony, they can place a card with a message written on it there, and then telescopes or satelites outside the colony could just zoom in on the window and snap a picture to receive information. Even if the colony has no windows, the spy could just then just get in a spacesuit, go 5 feet out the airlock and hold up the card. The spy going out the airlock could pose as a maintenance worker just doing a visual check of the exterior of the station or some piece of machinery or a valve or whatever. And data can be discreetly transmitted back and forth via laser. All of this could be done without using radio signals, so any monitoring of radio signals wouldn't give away that there is a spy on board.
I suppose a way to counteract that would be to have all windows and airlocks strictly monitored. Even so, the spy could try creating a small hole somewhere else in the station so he can show his message to the outside or put his laser transmitter/receiver in place, and the station would be huge enough that a small loss of air would be unnoticeable and pose little threat to the spy trying to do it.
Well I spoke to the last person how you might be able to have a police states wet dream by having mind reading tech but even without that, many of your ideas while theoretically possible are extremely unlikely to work.
First off if there were windows on the outside, well I guess it depends on how it is structured. Gundam and Elysium don't have artificial gravity, they make gravity by spinning, thus the outside walls of the space station are actually the floor, it'd be pretty weird to have a window on the floor like that, but maybe it's a weird luxury thing, but even so to make gravity it would have to spin very fast, a normal telescope even if it could see that far wouldn't be able to see, now they might be able to record it so they can pause the video when the window the message is at is seen. But again this would require alot of things to go right like I said earlier, assuming that there is an actual window on the ground, or that the area is not monitored. Because space colonies would probably have cameras everywhere except maybe personal rooms/houses.
As for the second part about going out on a space walk, that would probably require permission and be recorded and known about in advance. You can't just allow anyone to walk whenever they want put on a space suit then go depressurize a room to go on a space walk, what if someone doesn't know that room is depressurized and opens it dragging him and other people in that section into space? So no you or the bureaucracy or the AI would know that someone asked to go out, and then things would need to get ready, like a sign saying danger, etc. A spy couldn't walk it with a cardboard sign without security or the technicians who are controlling the airlock seeing it. And that last part about making a small hole is the most wrong. Space isn't completely empty, there are micro meteors, and other hazards, you don't want to allow a small break to accumulate. If there is a damage to the structure especially the outside walls that is letting even a tiny amount of air out that is a serious hazard and there should be systems to notice that there is a hole in the colony. There should even be a back up system or two because that is extremely important and you would want that fixed as soon as possible.
No I think a better way for a spy to let out information would be to throw out some kind of data packet that sends the information to whoever in the trash. That's assuming the colony would just deal with trash by throwing it out into space.
A space colony would not have American style freedoms you wouldn't have a right to nearly as much privacy, a space colony could not allow anyone to go Allah Ackbar because such an action would be a mass death event. Space colonies would be more similar to Japan, or China or other east Asian nations where the authorities can and will investigate you without a warrant, because depending on how the colony is made if it is one big section then it could kill everyone. If it has multiple sections then a bomb inside could wipe out everyone in that section.
