TLDR: The best we can claim is that the number of moves for black to force a win is bounded by the number of moves for black to force a win in a regular game of chess, a number that we don't know.
Consider the following position:
[FEN "8/1k5R/R7/1K6/8/8/8/8 - - - 0 1"]
We can then specify a winning solution for white like so.
- rg6
- rg8#
However, we can use this example to show that in order for white to have a winning strategy in this game, they must have a winning strategy for chess itself. To do so, let's consider how the solution above was generated.
We first consider all the possible moves for black. In this scenario, those are 1 ... kb8 and 1 ... kc8.
Since the problem doesn't provide us a way to conditionally specify a move other than determining whether the move is valid, we must specify a strategy that is winning regardless of what black plays in a situation.
Regardless of which move black chooses, 2 rg6 will be a valid move, thus we progress to a scenario where black's king is son the 8th rank and white has two rooks on the 7th. Neither can be reached by the king before being checkmated. On this turn, black can either play, 2 ... ka8 or 2 ... kc8 if they played 1 ... kb8; or they can play 2 ... kb8 or 2 ... kd8 if they played 1 ... kc8. We can picture this move set as a decision tree (this will be helpful when we go to generalize this situation). Regardless of what black plays on either of their turns, 3 rg8# is innevitable.
How did white select these moves? That's the natural question to ask, and we can build on our concept of a decision tree to do it. After each move by black we can envision a similar decision being made by white. Enumerating all of whites possible moves would be much more verbose, but certainly possible [1]. In each of these positions, we would then evaluate the position as white to determine if it led to a further winning strategy for white. We make a move if, regardless of what black does, there is a forced mate for white. This is the well known Minimax algorithm.
Call the position above P(n) where n is the move number of the game ending in this position. P(n+1) would be the position following this, as we've described above, and P(n+2) is checkmate.
Now let's talk about the answer to the question itself, P(0), also known as the start of a game of chess. There are 12 possible moves black could play on move 1. All of them are valid regardless of what move white made, and white must consider all of them at once to make their next move.
If for instance the game began 1 e4 d5, the move set specified by white on turn two could include 2 exd5 d4. We could also read this as, if black plays the Scandinavian defense, white plays the Scandinavian closed. Otherwise, white plays d4.
On each turn, white must enumerate all possible moves after all possible moves by black from the current position P(t) for some turn t otherwise they will lose. A sensible way to order these could be defined as the minimax sorting by number of moves until forced checkmate, and this is a more restricted problem to providing a minimax solution to chess itself. Therefore, the best we can claim is that the number of moves for black to force a win is bounded by the number of moves for black to force a win in a regular game of chess, a number that we don't know.
To answer the other two questions, since white must plan for all possible moves from black in order to avoid losing, there cannot be any unique strategies for black since that strategy would, by the definition of how white selects a strategy, be considered by white. Assuming black can see the move list ahead of time, they would simply see the strategies white attempts to employ for whatever they play (such as seeing their decision to play the closed Scandinavian presented above). If black is making optimal moves anyways, I think this is unlikely to affect their performance, however if the white player is playing at their skill level, they may be able to find a weakness in their play just as they would in a standard game of chess.
[1]: The rook on h7 would be able to move to any square on the h-file or 7th rank, the rook on a6 could move to any square on the a-file or the 6th rank, and the king could move to any of the surrounding squares except a6.
