Oh my god of course it's not, unless by government you mean something broader than the executive branch, in which case you have to include the judiciary too. The three separate powers is the foundation of western democracies.
Yes, a U.S. "administration" is the closest analogy to a "government" in the sense usually used in reference to parliamentary systems when talking about a particular leader's government or a change of government, as opposed to the government of the country ("Europe" is sort of beside the point here, as its more about form of government than geographic location.)
The agencies in the executive branch are 99% civil service people, not political appointees, and they don't change over every four years. The administration is the President, the cabinet, and political appointees, so I think that's the equivalent term.
I think that's correct in an academic sense. But in the day-to-day usage, I think Obama's “this administration” lined up pretty well with Cameron's “this government”.
The thing that changes in a change of "government" isn't the whole executive branch -- most parliamentary systems have a well-developed permanent civil service. What changes are the PM, cabinet, and some subordinate political rather than civil service officers. That's pretty much a precise parallel to a U.S. "administration", not the whole of the executive branch.
I think the distinction stems from the fact that in France for instance if I want to refer to all three branches I say "l'État", but obviously in the USA "the state" is something different. "Le gouvernement" is only the président and his ministres.
Roughly, but the nomenclature is different. It's kind of the opposite of metonymy, it's using the more general word ("government") to refer to the more specific thing (the current set of politicians in power).
No, it doesn’t. It refers to the executive. Whenever we complain about the poor quality of government, (the VA, DMV,) we’re complaining about an organ of the executive (be it federal, state or municipal).
Er, not in the US. E.G. "those government fat cats in Washington" is more likely to mean the Congress (or at least the Congressmen you don't like) than anything else.
In the US, "the government" refers to all three branches. When we complain about the poor quality of government, we're frequently talking about Congress, too.