Technically he could, I believe FIDE has a minimum rating increase of 1 point for the winner of a game with > 400 ELO advantage on their opponent. But if he broke 2900 by playing in minor tournaments against low rated amateur opponents no one would take it seriously that he broke 2900. Realistically many, maybe even all of the top players could push for record ELOs by only playing against players well below their level. But not only are the optics bad and the records would be looked at as illegitimate, it would take a lot of time playing long classical chess games against inferior opponents. Which is a major opportunity cost since their time would normally be spent playing in and studying for professional tournaments.

No, because he wouldn't get any points for beating opponents that much lower than him. There is no such thing as a fractional rating point, so if the points gain gets below 0.5 it just rounds down to zero.

Only if he never actually loses one. Which he really shouldn't, but at high numbers the probability of slipping up becomes non-negligible.

They would have to be demotivated, and Carlsen would have to never make a mistake causing huge loss of ratings points. And in reality they would be more motivated than by most of their other games, and Carlsen makes mistakes.