So, the rules say that I have to solve the puzzle for the run to be valid, but what should I do when I enter the level and the door is already open (and the puzzle can't be done)? Or better: how can I avoid this happening? Because so far it seems pretty random

If you have solved the level 7 puzzle previously, without refreshing the game, then the door will already be open. All you have to do is refresh the page.

That makes sense, thanks