Is it genuinely possible for white to checkmate black in this position?

"At the moment he was called over by one of the participants—or, even more so, when he observed the situation himself—was he unaware of the circumstances?"

• He was unaware of the result, though he might expect a draw, and of the results of other ongoing games that might affect master norms or money prizes, and of the time on the clock at the moment of the decisive mistake.

@tpr said ^

"At the moment he was called over by one of the participants—or, even more so, when he observed the situation himself—was he unaware of the circumstances?"

• He was unaware of the result, though he might expect a draw, and of the results of other ongoing games that might affect master norms or money prizes, and of the time on the clock at the moment of the decisive mistake.

You acknowledge that a checkmate in a knight-versus-bishop position can be overturned, depending on the circumstances.

Can a checkmate in a queen-versus-bishop position be overturned, depending on the circumstances?

"You acknowledge that a checkmate in a knight-versus-bishop position can be overturned, depending on the circumstances."

• Yes. It is not the checkmate per se, but the game result that can be overturned.

"Can a checkmate in a queen-versus-bishop position be overturned, depending on the circumstances?"

• Yes, e.g. when I have the queen and Carlsen has the bishop. It is not the checkmate per se, but the game result that can be overturned.

@tpr said ^

"At the moment he was called over by one of the participants—or, even more so, when he observed the situation himself—was he unaware of the circumstances?"

• He was unaware of the result, though he might expect a draw, and of the results of other ongoing games that might affect master norms or money prizes, and of the time on the clock at the moment of the decisive mistake.

No, we are looking specifically at these particular endgames.

Are there grounds for an arbiter to overturn a checkmate in a knight-versus-bishop endgame, or in a queen-versus-bishop endgame?

Do both of these scenarios fall under the following rule:

11.1 The players shall take no action that will bring the game of chess into disrepute.

Incidentally, there is no mention here of tournament standings or prize money.
That is merely your own speculation.
Imagine if, in the same tournament, one player were awarded a win in an identical endgame, while another were awarded a draw.
That would constitute bias on the part of the arbiter.
An arbiter must rule consistently—either declaring a checkmate or a draw in both cases.

"No, we are looking specifically at these particular endgames."
The rules about the endgames are clear: 5.1.2, 5.2.2, and 6.9.

"Are there grounds for an arbiter to overturn a checkmate in a knight-versus-bishop endgame, or in a queen-versus-bishop endgame? Do both of these scenarios fall under the following rule:
11.1 The players shall take no action that will bring the game of chess into disrepute."

• They can, depending on circumstances.

"there is no mention here of tournament standings or prize money"

• There is no definition of what an action that will bring the game of chess into disrepute entails, it is up to the arbiter to judge..

"one player were awarded a win in an identical endgame, while another were awarded a draw"

• The arbiter awards no win or draw, he can only overturn the game result if there are grounds 11.1 is applicable.

"An arbiter must rule consistently"

• Yes.

"declaring a checkmate or a draw in both cases."

• The arbiter does not declare checkmate or a draw, the rules 5.1.2, 5.2.2, and 6.9 do without arbiter intervention.
  The arbiter can only overturn the result of any finished game if 11.1 is applicable.
  He can use
  8.7 At the conclusion of the game both players shall indicate the result of the game by signing both scoresheets or approve the result on their electronic scoresheets. Even if incorrect, this result shall stand, unless the arbiter decides otherwise.

@tpr said ^

They can, depending on circumstances.

<There is no definition of what an action that will bring the game of chess into disrepute entails; it is up to the arbiter to judge.>

Yes. Prize money has absolutely nothing to do with this, as the rules of chess only take into account what happens on the board.

<They can, depending on circumstances.>

Name even one reason why a checkmate could be overturned in a queen-versus-bishop endgame.
You cited an example of a possible endgame in a game against Carlsen, but you didn’t explain why.
You merely tried to shift the responsibility onto the game as a whole—but that is a different topic.
We are discussing theoretical endgames—what is permissible to play, and what is not.

"Prize money has absolutely nothing to do with this"

• Article 11.1 includes foul play, and prize money can be an incentive for foul play.
  Master norms too: a grandmaster might sell a game so the opponent can score a master norm.
  Tournament standings too: say A plays B in a final round and both have 7/8. Behind them is C at 6.5/8. A and B feel fine with a draw, and play into K+B vs. K+N, but play on, just in case. Now C wins and comes at 7.5/9 and would have better tie breakers. So A and B no longer are fine with a draw. A wins by checkmate and wins the tournament.

"shift the responsibility onto the game as a whole"

• 11.1 is about the game as a whole and even behavior outside the game.

"theoretical endgames"

• 5.1.2, 5.2.2, and 6.9 apply. All play is permissible except in case of a dead position per 5.2.2.

@tpr said ^

"Prize money has absolutely nothing to do with this"

• Article 11.1 includes foul play, and prize money can be an incentive for foul play.
  Master norms too: a grandmaster might sell a game so the opponent can score a master norm.
  Tournament standings too: say A plays B in a final round and both have 7/8. Behind them is C at 6.5/8. A and B feel fine with a draw, and play into K+B vs. K+N, but play ...

<Master norms too: a grandmaster might sell a game so the opponent can score a master norm.
Tournament standings too: say A plays B in a final round and both have 7/8. Behind them is C at 6.5/8. A and B feel fine with a draw, and play into K+B vs. K+N, but play on, just in case. Now C wins and comes at 7.5/9 and would have better tie breakers. So A and B no longer are fine with a draw. A wins by checkmate and wins the tournament.>

And what complaints could there be against a player who has been checkmated?

Consider the same tournament scenario, but in an endgame of queen versus bishop.

In both cases, the opponent ends up being checkmated.

What objections might an arbiter raise in the first case, and what about in the second?

Strength of the players mean a lot. Queen vs bishop is easy checkmate for the queen and impossible for bishop. so nothing to do. BUT if a FIDE master wins K+B vs. K+N game against IM arbiter will in tournament qualified for norms arbiter will report to chief arbiter who will notify FIDE with Tournament Investigation form about suspect behaviour. At at Qualification commission + Ethics and Disciplinary Commission will handle. Qualification committee will make player norm void - also possible that whole tournament loses qualifications but that would require proof intentionality of the organizer. And ehtics commission would then consider if other means are necessary.

But if theo 1400 player play then accidents happen and there is no need to do anything

"What objections might an arbiter raise in the first case, and what about in the second?"

• The same: foul play, deliberately playing to lose i.e. matchfixing e.g. in exchange for money.