The highest rated person in classical chess is also the highest rated person in rapid and blitz chess and the reigning world champion in classical chess.
He's unquestionably the best player in the world. Right now, his competition is closing in on him, but they haven't caught him.
We don't know whether the peloton will reel in the leader or if the leader has an extra gear. I rather suspect Carlsen has extra gears.
Maybe so. Carlsen does have quite a large lead in the rapid and blitz ratings. I'm very curious to see where Kasparov falls, in the grand scheme of things though. I expect around 4th or 5th in the world in rapid and 5th in blitz. Just a guess. He's already proven that he can beat Nakamura.
You're assuming that Magnus is still the best player in the world. Kramnik, So, Aronian, Caruana and Mamedyarov are right on his @$$, as far as ratings go. I would put Kasparov in that group too.
The oldest active player over 2700 is 48. Kasparov is 54 and has been retired for over 10 years. You're thinking of Kasparov the legend, not Kasparov the man.
As far as Carlsen, yes, people are right on his @$$ and all it takes is for them to have career best performances and Carlsen to have the worst results he's had in many years... and he's still higher rated.
I don't know if you've checked the ratings lately, but he's like one loss away from being knocked off the top, in classical chess. He's only 10 points ahead of Kramnik, 12 ahead of So and 15 ahead of Caruana. Also, So and Caruana are both younger than Carslen. It could happen sooner than you think. I expect Wei Yi to pass him up eventually too. He's only 18 years old and is only 70 points behind Carslen now.