Question about Puzzle rating system

Hello,
Consider a player that has like 2500 puzzle Elo with a stable deviation, solving a very long puzzle (7 moves long) with a rating of 2600 Elo, and consider these 2 situations:

situation 1 : player gets the puzzle wrong in the first move
situation 2 : player gets the puzzle wrong after solving 6/7 moves

My question is will the player loses the same amount of points in the two situations or not? Likewise, is the puzzle gaining the same amount of points in the two situations?

yes, the player loses the same amount of points. yes, the puzzle is gaining the same amount of points.

puzzles are rated the same ways games are. consider these two scernarios:
situation 1: player gets mated on move 5.
situation 2: player times out in a winning position on move 150.
points are the same in both situations, for both the winner and the loser.

Thank you glbert for the precise answer.

Although I'm not quite sure I bought that...

Solve essentially means to complete the puzzle. If you get even one move wrong, you are failing to solve it and hence you don't get any points. Correct system.