Oh yes, they really do, you only have to look at what the majority of British newspapers are reporting to see what most British people believe.

https://en.wikipedia.org/wiki/List_of_newspapers_in_the_Unit...

Of course not, but it seems to be an inherent attribute of all politicians of all mainstream persuasions these days. So other than spoiling one's ballot, what to do?

Some do, especially on topics they don't know much about. And that would be the majority of the people.

Yes, so long as the government's actions ostensibly align with their own values.