I'll simply reply to the main question, and that'd probably be a reply to some of your sub-questions.
The main difference between actual proper tag teams and two thrown together superstars, is in the way they act.
A well formed tag team, would act as a tag team. Not just some generic "I like this guy", ""We're so happy to be tag team" kind of crap, like Sneaky Fart has been saying in their few interviews. Tag teams need to actually act as two people who are at least good friends. not just two people who slightly like each other at best. Naturally, they also need to have charisma as a team, which means at least one of them is good on the mic individually.
For an example of a thrown together tag-team you can take Air Boom, as I said earlier. Just listen to their interviews and look at the story they're telling.
For an example for a real tag team, take Awesome Truth. Listen to their interviews, look at their segments, and promos in the ring. They show synergy in all that, and actually look like 2 good friends (perhaps they're friends outside the ropes? Who knows..). I don't even need to mention Miz is a mazing on the mic, and Truth is good on the mic as well in his unique funny way.
As for why Awesome Truth isn't as good as The Kings of Wrestling, it's because they simply didn't have enough time to become great. They didn't have the opportunities to have any classic tag-team moments, like we know E&C, The Hardy Boys and others have had. Plus, in the current state of the WWE, they simply don't have any decent opponents to even create legendary moments with. Before that happens, the Tag Team devision needs to be reborn, and at least 3 other decent tag teams need to be added ( to be on the same brand).
As for why people call Awesome Truth a thrown together tag team, that's simple. Many people only come here for one reason - to complain, complain and complain a bit more. They're just what Eric Bishop defined as the "Ten Percenters", the most loud part of the IWC who think because they know a few business terms they suddenly understand every aspect of its work, and go on a complaining spree online. Believe me, there will always be people who call the next great thing "overrated", the next great tag team "thrown together" and so on.. (even though I don't think Awesome Truth will last long, due to a terrible tag-team division and Miz being too good as a singles competitor). Remember how more then half this forum couldn't stand The Miz earlier? Said that he should've stayed in the mid-card, WWE made a mistake pushing him, he's an upper-mid-carder at best? A year later, most of them now praise him, or simply agree that he's one of the top heels now and will be one of the faces of the WWE in the near future (a year or two). Just dont listen to them, but rather look at things yourself - your own judgment is worth just as much as anybodies' on this forum.