How well do you know the rules of chess?

Incorrect. If 10 or more moves have been played (by each player), which is clearly the case here, then the game continues as is. Once the game is finished, remember to tell the person recording the game scores about the wrong colours. If less than 10 moves had been played, then the game is restarted.

This rule applies to all time controls.

Incorrect. Any time a player's first illegal move is discovered while a classical game is still in progress, then the arbiter must reinstate the most recent legal position that can be determined by discussion with the players and checking of the scoresheets. Since such checking might be distracting to nearby players, the arbiter might choose to do it with the players in another area.  In all time formats, the first illegal move will only incur a time penalty for the offending player (two minutes in classical; one minute in blitz/rapid). It is only the second illegal move that leads to an automatic loss.

Incorrect. White can castle because in position 1 because the king is neither moving into check, nor crossing a square threatened by one of black pieces. The rook is always allowed to move onto or across a threatened square. In position 2, castling is not allowed because the king is crossing the threatened square d1.

Incorrect. In this case, your opponent’s eagerness to win has worked against their own interests. As per FIDE rules there is a distinction between “making” a move and “completing” a move. A move is “made” when you release your piece on the target square. A move is subsequently “completed” when you hit the clock. For the purposes of judging whether a move is illegal, it must have been completed.

This rule applies to all time controls.

Incorrect. If an arbiter sees you make an an illegal move in a blitz (or rapid) game, they can only point it out before your opponent has made their move. Once your opponent has responded by making a move, the arbiter cannot intervene. If they do, you should ask for another arbiter’s intervention, and if that does not solve the problem, you can lodge an appeal later. However, the players themselves can decide to correct the illegal move, without the intervention of the arbiter.

In a classical game, however, if a player or arbiter becomes aware of an illegal move that occurred earlier (regardless of how much earlier), then the position immediately before the illegal move must be reinstated (or as close to it as is possible).

Incorrect. In this type of incorrect set-up, all the pieces are nevertheless still in their correct positions relative to each other. So, the position can be set-up on a properly oriented board, without any impact on the strength of either player’s position.

In a blitz or rapid game, the pieces would not be transferred to a correctly oriented board (i.e the game continues as it is), because such transfers only are done if less than 10 moves have been made.

Incorrect. As per FIDE rules, this is a win for black. While it is indeed true that white would need to cooperate to allow black to achieve a checkmate, this does not matter. The game is only drawn “if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.” So, the governing principle is not whether checkmate can be achieved by normal play, but whether it can occur by legal play. That is the case here (see the position below). Note that not all arbiters agree with this rule, and if the tournament is not FIDE-rated, they might inform players (at the start of tournament) that they are applying the principle of ‘by normal play’ instead.

This rule applies to all time controls.

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Incorrect. The only move that would not be judged as illegal is where you move the pawn with one hand and hit the clock with the other. This is however still considered an offence, but there are many offences (such as disruptive behaviour) that do not make a move illegal. You could still be warned by the arbiter, and perhaps even penalised in some way, but you would not be in immediate danger of losing the game if, for example, this was the second time the arbiter had warned you about the behaviour.

The illegal features of the other ones are as follows:

1. When  capturing a piece, you must use the same hand for both removing the piece and moving your own piece onto the captured piece's square.

2. It is illegal to make a move that leaves your king in check.

3. When promoting a pawn, you must place the new piece onto the promotion square before you hit the clock. By not doing so, your opponent's thinking time is compromised by the distraction of you placing the new piece, and, in some cases, the uncertainty about which piece you will choose to promote.

These rules applies to all time controls.

Incorrect. When promoting a pawn, the touch move rule does not apply. You only become committed to using a chosen piece when that piece comes into contact with the promotion square. That did not occur in this case, so you are within your rights to change your mind, and neither is this change of mind considered a distraction worthy of any penalty.

This rule applies to all time controls.

Incorrect. As long as the game has not involved any illegal moves, once a checkmate is on the board, the result stands. Therefore, your loss is final. This rule applies to all time controls.

If the incorrect set-up was noted before a checkmate (or draw) had occurred, then the game must be restarted. This is also the case in a rapid or blitz game, but only if less than 10 moves have been made. Otherwise, the game continues.