2. You are completely wrong on this claim. Eurosceptics overwhelmingly vote. It's the mainstream that "sleeps" in the European elections. It's a very well documented fact that European elections are more populist than mainstream and as a result of less mainstream voters, a lot of small parties that don't have enough mainstream support to push through in local general elections can still get their candidates elected. We're seeing it here in Finland right now, when a populist right wing politician gathered most votes and his party gave him a PM post. As a result, party crashed in popularity because mainstream voters turned their backs on him and his populist agenda. Same thing happened to True Finns, who trailblazed to ~20% of vote in European election on Eurosceptic agenda, and are almost a quarter less popular in mainstream local elections just a bit later. Local elections factually have more voters because a lot of mainstream voters who view EU as too remote and inconsequential vote in local elections.
This is factual, and almost every country in Europe has concrete examples of this, on all sides of political spectrum.