Do they vote for as many electoral offices and ballot propositions at the same time as is typical in American elections? Comparing American and European election mechanisms is like comparing a truck with a bicycle.
Not sure. In UK often local, European and e.g. police commissioner elections will be held on the same day. But these are handled using multiple ballot papers. So the counting process scales purely horizontally.
Exit polls are instant. The national implications of elections are usually declared around 3-5am (counting starts around 10pm). The last constituencies usual declare by midday the next day. In the last UK general one constituency took two days - there were about 12 votes between the top two parties so they did a few recounts.