If a candidate wins the popular vote of a state, do they then earn the electoral votes of that state?

The electors almost always vote the way the voters voted. BUT in some states, all the electoral votes go to the candidate who got the most votes, while in some, the electoral votes are apportioned according to the vote. So in my state, if candidate A gets 51% of the vote and candidate B gets 49%, ALL of the electoral votes for to candidate A, and the other votes are meaningless.

Theoretically, an elector can vote for whomever he or she chooses. In practice, the electors follow how their state voted. Some states mandate it to be so legally.

Yes and yes. Except in Maine and Nebraska, but the way they do it also normally results in the same thing - if a candidate wins the popular vote in a state, the state chooses the slate of electors their party selected, who are of course all pledged to vote for that candidate. Even if the candidate only won the popular vote by one vote, they've won the state and the state will choose their slate of electors. The constitution doesn't actually say how the states should choose their electors, but in reality that's what they all do.

Electors can vote for who they want and occasionally one doesn't vote for who they pledged to support. That's a faithless elector. But that's very rare, which is why it's possible for TV election night coverage to say who's won this state and that state, keep count of the electoral votes, and confidently say who will be President once enough states have been counted for us to know who definitely has the magic unbeatable 270 electoral votes. Even though the electoral college hasn't voted yet. We KNOW how it will vote apart from the odd faithless elector.

The constitution provides for an electoral college that consists of real people because that was what the drafters came up with in 1787. There's no reason why it should now, when all the states choose their electors according to the popular vote (they didn't all do it that way back then - did you know South Carolina didn't have presidential elections until after the Civil War?) It could be a virtual college, with no real electors at all. Each state just has its number of electoral votes decided by the way the people of that state vote, and then you'd never have faithless electors.

But that would take an Amendment, and faithless electors have never made any difference to the actual result. Which is maybe why nobody much is interested in changing it.

yes popular vote is the winner of all the electorial votes.

Yes. In 48 states, plus Washington DC, the winner of the popular vote in the state gets ALL of that state's electoral votes. Maine and Nebraska do things a little differently. They give two electoral votes to the overall winner in the state and then give out the remaining electoral votes based on who wins each of the state's congressional districts. The electors don't exercise individual judgment in choosing the president. In fact, the electors who assemble will depend on how the popular vote goes. When we vote we're actually, technically, voting for the electors for a candidate. There's lots of different electors out there, from ordinary citizens to politicians like Bill Clinton. Aside from laws which dictate how electors vote, they're normally chosen for loyalty to their party.

Each candidate has his/her own slate of Electors. Whomever wins the popular vote, it is their Electors that get picked. Donald Trump Jr. is an Elector, so is Bill Clinton.