I don’t know about the whole of Europe but generally, no. The government is the executive branch or a subset of it.

Interesting -- is there any term referring to the executive, legislative, and judicial functions collectively?

I skimmed the constitution of my country (Italy) and there is no collective term. There is a section "Organization of the Republic" that lists the several components (Parliament, President, Government, etc.) When we say Government we refer only to the Prime Minister, the other Ministers and their staff.

I am not sure. In French that would be the state (L’État). It’s more complicated in the U.K., with its layers of national, devolved country, and local governance. Then, it would be different again in federations like Germany.

"The state apparatus" (or "the state" for short).

"State and government" section in https://en.wikipedia.org/wiki/State_(polity)

Authorities?