There’s a lot in here, and there are a lot of rules that directly apply. Regarding the improperly set clock:
16O. Defective clocks.
Every indication given by a clock is considered to be conclusive in the absence of evident defects. A player who wishes to claim any such defect must do so as soon as aware of it. A clock with an obvious defect should be replaced, and the time used by each player up to that time should be indicated on the new clock as accurately as possible.
The director should use judgment in determining what times shall be shown on the new clock.
…
16P. Erroneously set clocks.
An erroneously set clock should be handled in the same fashion as a defective clock. As in 16O, the director should use judgment in deciding whether to make time adjustments.
So, for your first three bullets, related to the clock problem: you can totally ignore the clock being improperly set since neither player noticed it.
13C5. How to claim.
To claim a win by time forfeit, a player should stop both clocks (5I) and state the claim. If the opponent accepts the claim, the game is over. If the opponent does not accept the claim, the claimant must present the claim to a director.
For your fourth bullet, for the flag call with 35 seconds: it was an improper (and inaccurate) claim to claim flag fall while Player B still had 35 seconds and without stopping the clock, but the escalation to a director step wasn’t taken so it’s a moot point.
11D1. Illegal move in time pressure.
Time pressure is defined as a situation where either player has less than five minutes left in a time control and the time control does not include an increment or delay of 30 seconds or more. A director should not call attention to illegal moves in time pressure, only the players may make that claim.
For your fifth bullet, the illegal moves: only Player B could handle this.
9E. Checkmate or stalemate.
In the case of a legal move which produces checkmate (13A, 4A) or stalemate (14A), the move is determined with no possibility of change upon release as described in 9A, 9B, 9C, or 9D, whichever applies. The move is completed simultaneously with its determination.
13A3. Unclear if checkmate or flag fall came first.
After considering all available evidence, including testimony by the players and any witnesses, a director who is still unable to decide whether the claim of the flag fall occurred first shall deny the time claim and rule the checkmate valid.
For your sixth bullet, about the checkmate: you need to be clearer here. Either the mating move was completed or it was not completed, and that determines whether the result is a win for Player B or a draw. If it’s not clear, the checkmate wins.
The seventh bullet, about the delay, is answered as with the first three bullets: it’s the players’ responsibility to call that.
The eighth bullet, about Player A forfeiting, looks like a personal problem.
It’s not technically a draw. It’s a draw per the rules if the flag claim was made before the mating move was completed, and it’s a win per the rules if it wasn’t, with a tie being resolved in favor of a win.
14J. Draw declared by director.
On rare occasions the director may encounter a situation in which a ruling is required and a decision in favor of either player would be unfair to the opponent (for examples see 20E2d and 20E2h). In such situations the director may rule a draw on the grounds that this is more equitable (i.e., less inequitable) than any other ruling.
Regarding your question of TD discretion - technically it exists to declare the game a draw, but this does not seem to be that rare occasion in my opinion.