I'm not the person you replied to, but just wanted to add something to help answer Q2. Communicating information to a large fraction of the populace is generally pretty hard because there are so many memes competing for attention, and true information doesn't necessarily spread faster than false information. Even so, it's pretty much common knowledge that the Iraq war was based on a falsehood, so communication does work well enough at least some of the time. Okay, so suppose we now collectively know that most politicians are liars and will have no issue with lying when it's convenient for them and they expect to get away with it. I think it's very common to find people who think this in western countries, actually.

Now how do we vote in such a way as to make sure we elect non-liars? Being a liar is not always visible, but maybe we can determine it by looking at whether the candidate lied while holding previous offices, and whether or not they get caught in any lies while on the campaign trail. We may also be able to make some judgment of a person's honesty based on how they make arguments, i.e. how they use statistics, and how often they omit relevant information that would look bad for them.

So suppose that everyone could perfectly identify who was a liar and who was honest. Would the electorate then vote only for honest politicians? Nope. A voter finds other things valuable in a politician besides just honesty, for example agreement on policy issues, or allocating tax money in a way that benefits the voter. Even if the candidate for party A is found out to be a no-good stinking liar, that still might not be enough to induce a party A voter to vote for the party B candidate instead. After all, party B is terrible. And there can be no party C that adopts the policy stances of party A but is staffed by honest politicians. Because of vote splitting in first-past-the-post electoral systems, two parties tend to dominate with outsiders having no chance of getting elected, even if the electorate prefers the outsiders. This is why we'd ideally want to use a more sane electoral system like score voting.