"United Earth" could mean that the entire Earth is united, in the same way that "United Nations" means all nations are united.
Or, in the context of UESPA at least, it could be an outright lie. Nothing wrong with those - say, Pan Am wasn't "pan-American" in any real sense, regardless of whether we talk about the Americas, just North America, or merely the United States of America.
Indeed, "United States of America" doesn't cover much of America, come to think of it. Perhaps "Earth" has more specific meanings than just "this big ball in the sky / beneath our feet" in these contexts, too?
That 2079 scene might not have taken place in America.
If anything, the regalia look a bit British. Beyond that, all we can say is that both the judge, the rabble and the various workers of the court appear generic Caucasian, save for those Asiatic gong-players ("trained monkeys"/downtrodden slaves?).
It was probably an ECON court, anyway.
Why?
Nothing suggest Cochrane had anywhere near that amount of resources available for what would be a far more complex development.
Except, of course, the fact that the development was a splendid success.
He literally designed and built such a craft in, more or less, one fell swoop. Launched it and hit his goal the first time.
Based on what?
Nothing in the movie says "Cochrane did it all alone" or "Cochrane did it in a day, between drinks". The exact opposite is explicitly stated: this is a decades-long project that has stalled because of the war. Nothing wrong with that.
Consider that after Cochrane, it took the humans about 80 years to break past warp 2 to warp 3.
Well, it took that long for Henry Archer's engine to break past warp 2 to warp 3. Doesn't mean that Earth didn't possess (or at least rent) plenty of Rigelian warp 4 spacecraft (but trying to reverse engineer the engine would have meant the Rigelians would have incinerated Earth), or that some other team didn't already operate indigenous warp 3 hardware (with no potential for ever reaching warp 5, the real goal of Archer's team).
Warp 2, for all its speed, is still many months to years between star systems.
All we know is that it is months to years between systems of interest to merchants. It might take a warp two spaceship just two days to get from here to Alpha Centauri, though. In TOS, warp two sounds like a fairly viable interstellar speed that Kirk himself often uses, at least for parts of his interstellar hops.
Yet a warp drive like that would, in theory, make interplanetary travel much easier...if you could manage to avoid killing yourself by running into grains of sand at light speed. Earth to Mars in minutes rather than days, weeks, or months. Pluto and back within two hours.
"Demons"/"Terra Prime" shows Earth operating insystem mining platforms that have just this type of warp drive. We probably shouldn't assume it was a secretly installed superpower, but rather a routine and vital system for such rigs in general.
Timo Saloniemi