We saw exactly how you're supposed to turn on the barrier when Adlet demonstrated it at the replica - place sword in stand, place hand on tablet, say words.
I think it is a bit of a stretch to say Nashe could have done that while being with the other 3 fighting off monsters. Sure, she could move the sword, but what about the rest?
Given how much they hyped this door/seal, it pretty much has to be Maura, the woman with the key, and you must be able to close the door with the key.
As for the "why", I have no idea.
We just don't know enough about the 3 newcomers to know any potential motives, or even their means if they have special abilities.