That'll be very little help if the perfect game you have starts with 1.e4, but Magnus plays 1.d4. Yes, you're not losing, congratulations. You're still on your own against Carlsen now.
You can just evaluate whether or not a given move will change from a +1 or 0 position to a 0 or -1 position and play it from there.
Perfect play in a perfect game means that the objective won't change - in optimal control theory this is called Pontryagin's Maximum Principle or the Bellman optimality criteria. A "value to go" function is enough to find the optimal solution.
Yes, but we were talking about a scenario where someone was just given the moves of a single perfect game. Not an oracle that gives you the -1/0/+1 of any position.
Weakly solving a game requires a proof of optimality, which means an evaluation of all variations to prove their value. A sequence of moves in one perfect game isn't weakly solving a game.
