That's how you get Brexit.
Nope. GP is disagreeing with direct democracy, a very specific type of government which is not usually in favor nowadays. Most democracies in the world are representative democracies, where you vote for people who then vote on issues.
If there is no way to elect a representative that would support certain idea, then the system is not a democracy but something defined by the method which is used to restrict the pool of available ideas or representatives.
For most democracies in the world such a method was control of mass media, but now they have either to become real democracies or find another method of pretending to be a democracy.
Not necessarily. It is very well possible for people to vote for representative they hold in high esteem even though they do not agree with them on several matters. It is very possible for representative to go against what is the current majority opinion, and even be reelected afterwards, because in the meanwhile theirs choices have bee proven right. That's why in representative democracies there are elections for a certain role only every several years, to decrease the relevance of immediate issues on the vote, and give more importance to other factors such as broader ideals and the trustworthiness of the candidate.
You can very well prefer direct democracy, but it is not the only, or the one true, kind of democracy.
reducing complex trade-offs to a single vote for Team A or Team B is exactly what could be avoided with an issue-specific, liquid democratic system with a process for participatory, public discourse to achieve compromise