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.)

I would say “the executive branch”

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.

Yes.