Are multiple scripts needed if I put multiple of the same type of puzzle in a level?

If I were to put 2 or more of the same type of puzzle in a level and require them all to be completed to win the level, would I need to have a script for each one? or would I just use a tally system to determine if the puzzles are complete or not to open a door, I think I know how to change the required ammount of completed puzzles to open the door, I just need to know if I am correct.

No. Just as you wouldn’t need separate rulebooks for different levels in a board game.

What’s the win condition? Occupy all blocks of a specific color? Destroy all enemies? Remove at least ‘n’ blocks?

All of that is one rule, or a combination of rules, not separate scripts. The scripts wouldn’t check for 3,6 and 7,4 and 9,1 coordinates to be occupied for instance but rather have a list of spaces that need to be occupied, and the occupation is recorded (or removed) as the game progresses.